Time-invariant Control Research Articles

OCTUNE: Optimal Control Tuning Using Real-Time Data with Algorithm and Experimental Results

Autonomous robots require control tuning to optimize their performance, such as optimal trajectory tracking. Controllers, such as the Proportional-Integral-Derivative (PID) controller, which are commonly used in robots, are usually tuned by a cumbersome manual process or offline data-driven methods. Both approaches must be repeated if the system configuration changes or becomes exposed to new environmental conditions. In this work, we propose a novel algorithm that can perform online optimal control tuning (OCTUNE) of a discrete linear time-invariant (LTI) controller in a classical feedback system without the knowledge of the plant dynamics. The OCTUNE algorithm uses the backpropagation optimization technique to optimize the controller parameters. Furthermore, convergence guarantees are derived using the Lyapunov stability theory to ensure stable iterative tuning using real-time data. We validate the algorithm in realistic simulations of a quadcopter model with PID controllers using the known Gazebo simulator and a real quadcopter platform. Simulations and actual experiment results show that OCTUNE can be effectively used to automatically tune the UAV PID controllers in real-time, with guaranteed convergence. Finally, we provide an open-source implementation of the OCTUNE algorithm, which can be adapted for different applications.

Formula omitted] gain-scheduled state-feedback design with experimental validation in a control moment gyroscope represented as a polynomial LPV model

The main contribution of this paper is a new H2 gain-scheduled state-feedback synthesis condition for continuous-time linear parameter-varying (LPV) systems where the parameters have bounded rates of variation. The matrices of the model as well as the control gain can have arbitrary polynomial dependence on the time-varying parameters. The synthesis conditions are formulated in terms of LMI relaxations combined with a search in a bounded scalar parameter, which can be used to obtain controllers with improved performance. As an experimental validation of the results, gain-scheduled controllers are designed and applied to a control moment gyroscope modeled as an LPV system with polynomial dependence on the time-varying parameters. Comparisons with a time-invariant controller, designed with the same performance criterion, are presented to illustrate the advantages of the proposed approach.

Linear Parameter Varying Models-Based Gain-Scheduling Control for Lane Keeping System With Parameter Reduction

In this paper, a robust <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mathcal {H}_{2}$ </tex-math></inline-formula> controller based on Linear Parameter Varying (LPV) model with scheduling variable reduction is applied for a lane-keeping system. On a curved road section, varying longitudinal speed and roll motion lead to multiple parameter variations in the lateral vehicle dynamics. To trade-off between the complexity of the multiple scheduling variables and the accuracy of the LPV model, an order reducing method by Autoencoder (AE) is performed to obtain a reduced model and diminishes the conservatism of LPV-based controller design. Further, to ensure the continuous convex set membership of the reduced scheduling variables in online test scenarios, the Lipschitz constant of the offline trained neural network (NN) is tightly estimated by solving a Semidefinite Program (SDP). The convex set of local Linear Time-Invariant (LTI) controllers is designed according to the estimated Lipschitz bound of the trained NN. The LPV-based robust <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mathcal {H}_{2}$ </tex-math></inline-formula> feedback controller is then designed by solving a set of Linear Matrix Inequalities (LMIs). Numerical simulations with full vehicle dynamics from CarSim are given to demonstrate the performance of the proposed system on various test roads. The continuous finding of the reduced scheduling variable membership is guaranteed in the online tests, and the effectiveness of the proposed method is confirmed with the mean value of lateral offset error reduced by about 50% compared with LTI-based <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mathcal {H}_{2}$ </tex-math></inline-formula> controllers.

Stealthy attacks and attack-resilient interval observers

Industrial control systems have been frequent targets of cyber attacks during the last decade. Adversaries can hinder the safe operation of these systems by tampering with their sensors and actuators, while ensuring that the monitoring systems are not able to detect such attacks in time. This paper presents methods to design and overcome stealthy attacks on linear time-invariant control systems that estimate their state using an interval observer, in the presence of unknown but bounded noise and perturbations. We analyze scenarios in which a malicious agent compromises the sensors and/or the actuators of the system with additive attack signals to steer the state estimate outside of the bounds provided by the interval observer. We first show that maximally disruptive attack sequences that remain undetected by a linear monitor can be computed recursively via linear programming. We then design an attack-resilient interval observer for the system’s state, identifying sufficient conditions on the sensor data for such an observer to be realizable. We propose a computational method to determine optimal observer gains using semi-definite programming and compute bounds for the unknown attack signal as well. In numerical simulations, we illustrate and compare the ability of such interval observers to still provide accurate estimates when under attack.

Distinguishability criteria of conformable hybrid linear systems

AbstractWe relate this article to the emerging idea of distinguishability of conformable linear hybrid time-invariant control systems. To obtain the necessary and sufficient conditions ofα\alpha-distinguishability for fractional cases, we develop the Leibnitz rule for conformable derivatives. Furthermore, with the help of a study of Laplace techniques, a more simple criterion ofα\alpha-distinguishability for the fractional linear system is developed.

Conversion From Unstructured LTI Controllers to Observer-Structured Ones for LPV Systems

This paper considers the conversion problem from unstructured linear time-invariant (LTI) controllers to observer-structured LTI controllers, whose structure is similar to but not exactly the same as the so-called “Luenberger observer–based controllers,” for linear parameter-varying (LPV) plant systems. In contrast to Luenberger observer–based controllers, observer-structured LTI controllers can be defined and constructed even if the plant systems are given as LPV systems. In the conversion problem, the state-space matrices of the observer-structured LTI controller are parameterized with those of the given unstructured LTI controller, one free matrix, and a state transformation matrix. We also show a method to obtain the optimal state transformation matrix with respect to the convergence of the discrepancy between the plant state and the observer-structured controller state for a stochastically defined non-zero initial plant state. Several toy examples are included to illustrate the effectiveness and the usefulness of observer-structured LTI controllers, and the utility of the proposed conversion parametrization.

Decoupling fault detection vectors for fault detection in the TS fuzzy system

ABSTRACT The parity space method can be applied to detect the fault of the time-invariant control system simply and effectively. However, the parity space method is greatly limited in the time-variant system. Therefore, in this paper, a TS fuzzy system is used to describe this kind of system. The system parameters are obtained based on TS fuzzy rules, and the decoupled fault detection vectors for different channels are designed. Using this vector, the residual representing fault information is extracted directly. Ideally, the fault detection of different channels is decoupled. However, sometimes the fully decoupled detection vector cannot be designed, then a suboptimal decoupled fault detection vector is proposed. Simulation and verification are carried out on a steady-state system and a TS fuzzy system.

Stochastic Event-Triggered H∞ Control for Networked Systems Under Denial of Service Attacks

This article presents a novel stochastic event-triggered communication scheme (SETS) and a switching-like <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$H_{\infty }$ </tex-math></inline-formula> control method for networked control systems (NCSs) through an open bandwidth-limited network. To overcome the stochastic Denial of Service (DoS) attacks and save the limited network resource, a SETS is first proposed to decrease the number of packets transmitted while considering the malicious DoS attacks. Compared with the existing event-triggered schemes under a precondition that all triggered packets must be successfully transmitted, the proposed SETS has outstanding flexibility since it allows part event-triggered packets to be lost during the communication process. To fully use the dynamic features of communication in an open network, a switching-like control scheme is well designed, which can actively choose the different controller gains based on the current network Quality of Services (QoSs). Then, a networked closed-loop model is constructed, which considered both the effects of SETS and stochastic DoS attacks in a unified framework. Sufficient conditions for the existence of the switching-like controller are presented to ensure the stability of the networked control system while achieving the prescribed performance index. Gain matrices of the desired switching-like controller and the SETS parameters are reached in the light of the solutions to certain matrix inequalities. Compared with the existing time-invariant control strategy in a transmission interval, higher control performance can be expected since both the dynamic network information and the latest available state are well considered in the proposed communication and control framework. Finally, an illustrative example is given to verify the effectiveness of the proposed scheme.

Decentralized Implementation of a Class of Centralized LTI Controllers for Two-Channel Systems Using Periodic Control

Given a centralized linear time-invariant (LTI) controller, this article investigates if and when the same can be implemented in a decentralized fashion using continuous-time, high-frequency, periodic controllers, recently reported in literature, without compromising input–output performance in averaged sense. In this regard, it is shown that for a strongly connected two-channel system having each subsystem of equal sizes, there exists a relation to compute the decentralized periodic controller gains in terms of the gains of a given centralized LTI controller if the latter is minimum-phase, stable, and satisfies some relative degree conditions. A method to satisfy this relative degree constraint while designing the centralized LTI controller is developed. A suitable example is considered to show that the proposed decentralized periodic controller can mimic a centralized LTI controller in averaged sense. At the end, it is found that the proposed decentralized periodic controller, however, does not have enough number of periodic gains to obtain the above relation to compute its parameters for systems with more than two channels.

Designing and validating a robust adaptive neuromodulation algorithm for closed-loop control of brain states

Objective. Neuromodulation systems that use closed-loop brain stimulation to control brain states can provide new therapies for brain disorders. To date, closed-loop brain stimulation has largely used linear time-invariant controllers. However, nonlinear time-varying brain network dynamics and external disturbances can appear during real-time stimulation, collectively leading to real-time model uncertainty. Real-time model uncertainty can degrade the performance or even cause instability of time-invariant controllers. Three problems need to be resolved to enable accurate and stable control under model uncertainty. First, an adaptive controller is needed to track the model uncertainty. Second, the adaptive controller additionally needs to be robust to noise and disturbances. Third, theoretical analyses of stability and robustness are needed as prerequisites for stable operation of the controller in practical applications. Approach. We develop a robust adaptive neuromodulation algorithm that solves the above three problems. First, we develop a state-space brain network model that explicitly includes nonlinear terms of real-time model uncertainty and design an adaptive controller to track and cancel the model uncertainty. Second, to improve the robustness of the adaptive controller, we design two linear filters to increase steady-state control accuracy and reduce sensitivity to high-frequency noise and disturbances. Third, we conduct theoretical analyses to prove the stability of the neuromodulation algorithm and establish a trade-off between stability and robustness, which we further use to optimize the algorithm design. Finally, we validate the algorithm using comprehensive Monte Carlo simulations that span a broad range of model nonlinearity, uncertainty, and complexity. Main results. The robust adaptive neuromodulation algorithm accurately tracks various types of target brain state trajectories, enables stable and robust control, and significantly outperforms state-of-the-art neuromodulation algorithms. Significance. Our algorithm has implications for future designs of precise, stable, and robust closed-loop brain stimulation systems to treat brain disorders and facilitate brain functions.

Design of Observer-Structured H∞ Flight Controllers Converted from Unstructured Conventional H∞ Flight Controllers

We address the conversion problem from a priori designed unstructured Linear Time-Invariant (LTI) controllers to observer-structured LTI controllers, whose structure is similar to but is not exactly the same as the so-called “Luenberger observer-based controllers”, for Linear Parameter-Varying (LPV) or LTI Parameter-Dependent (LTIPD) plant systems. For this problem, we propose a method by designing appropriate state transformation matrices which minimize the errors between plant systems’ states and transformed controllers’ states for external inputs via parametrically multi-affine Linear Matrix Inequality (LMI) conditions. The proposed method embeds existing LTI controllers with the ability of observers while their control performance is unchanged. We introduce a numerical example and illustrate the usefulness of our method by embedding observer property to an a priori designed H∞ flight controller.

Quadratic Stabilization of Takagi-Sugeno Fuzzy Discrete-time Uncertain Networked Systems

For one class of Takagi-Sugeno uncertain time-delay discrete-time systems this paper proposes an extended way to account related constraints in problem solving of the networked control system quadratic stability reflecting sensor drifts and communication delays. The new design conditions are proposed, exploiting a set of linear matrix inequalities to guaranty the closed-loop system quadratic stability where a specific Lyapunov-Krasovskii functional is exploited. Combining into the functional the disturbance transfer function H∞ norm upper bound, the design task is defined as a multi-objective robust control problem, while only the set of time-invariant control law gains are used in the fuzzy parallel structure of the controller realization. A numerical example is included to assess the feasibility of the technique and its applicability.

Robust cascaded horizontal-plane trajectory tracking for fixed-wing unmanned aerial vehicles

This paper investigates the problem of horizontal-plane trajectory tracking for fixed-wing unmanned aerial vehicles(UAVs) subjected to external disturbances and uncertainties including coupling and unmodeled dynamics. Under the assumption there exist ideal inner-loop controllers, the 12-state model is reduced to a 6-state translational motion model, which is described by a group of simplified nonlinear equations with equivalent disturbances via introducing general aerodynamic models. Then a new cascaded control structure consisting of an outer-loop controller for position control and inner-loop controllers for attitude and thrust control is proposed. Based on feedback linearization technology and signal compensation theory, the proposed controller applied for position control incorporates a nominal linear time-invariant controller and a robust compensator, the latter of which is introduced to restrain the effects of uncertainties and disturbances. The robust performance of the closed-loop system is proved. Actual experimental results conducted on a small fixed-wing aircraft demonstrate that the proposed control approach is effective.

The impact of COVID-19 on the safety, housing stability, and mental health of unstably housed domestic violence survivors.

Using data from an ongoing longitudinal study, we examined the impact of the COVID‐19 stay‐at‐home orders on a racially diverse population of unstably housed domestic violence (DV) survivors over time. Specifically, we examined survivors' safety, housing stability, and mental health before, during, and after the onset of COVID‐19, and how demographic, social, and familial factors attenuated or exacerbated the effect of the stay‐at‐home orders. Approximately 300 participants were initially interviewed after they sought services from a DV agency, and then again, every 6 months over 2 years. COVID‐19 stay‐at‐home orders occurred midway through the completion of this multi‐year study. Longitudinal mixed effects models were estimated to examine the impact of COVID‐19 on the safety, housing stability, and mental health of survivors over time. We also examined models with several time‐varying (e.g., employment, income, social support, and number of children) and time‐invariant (baseline outcome scores, racial/ethnic identity, education, and disability status) control variables. Results revealed that safety, housing stability and mental health were improving for study participants before the onset of the COVID‐19 pandemic but plateaued after the stay‐at‐home orders were issued. Experiences of abuse, housing instability, and mental health symptomatology did not worsen as a result of the COVID‐19 stay‐at‐home orders. Notably, social support and housing services emerged as important predictors of outcomes, such that participants who received housing‐related services and greater social support reported less abuse, less housing instability, and lower mental health distress. COVID‐19 temporarily disrupted the positive trajectory unstably housed DV survivors were experiencing in regard to safety, housing stability and mental health. These findings provide critical insight into the importance of service access during and after global catastrophes. Additional resources and support may be helpful in assisting survivors to return to their pre‐pandemic recovery and growth trajectories.

Decentralized periodic control of interconnected systems with fixed modes

It is well known that decentralized linear time-invariant controllers fail to stabilize interconnected systems with unstable decentralized fixed modes. This paper employs a high-frequency (ω), continuous-time, linear periodic controller to solve this problem. In addition to handling a general class of strongly connected systems, the proposed controller ensures negligible ripples (O(1/ω) at most) in the plant output, unlike O(1) ripples with the existing ones. An H∞-loop-transfer-recovery based sequential method is used to design the controller in such a way that it achieves some centralized linear quadratic performance along with some desired loop properties in averaged sense. The results are illustrated using a suitable example.

An Application of the Z-Transform in Extracting the Density Regulation from the Periodic Output of an Age-Structured Population Model

The application of the Z-transform, a manipulation tool from the discrete signal processing (DSP) toolbox, on an ecological model was motivated by the mathematical similarities between an age-structured fish population model with a non linear density regulation and a linear time invariant (LTI) control system. Both models include a switching mechanism in regulating stock/signal throughput in accordance with a given density limitation/set value and both models can be expressed in terms of a negative feedback loop difference equations (Getz &amp; Haight,1989; °Astr¨om &amp; Murray, 2008). In the fish model, the switching mechanism is a density regulated stock-recruitment (SR) function which models the strategies implemented by the population in keeping the vulnerable egg-larvaejuvenile densities within an environmental limitation thereof (Subbey et al, 2014). A switching mechanism is also present in control engineering, for example, in the mechanism associated with cruise control in cars which keeps traveling speed close to a chosen set value midst varying weather and road conditions (Antsaklis and Gao, 2005). In both cases, the choosing of the control action and the tuning of its parameters requires careful consideration to avoid failures such as incorrectly timed switching actions in a control plant (see Kuphaldt (2019)) and errors in estimating total allowable catch (TAC) in the fishing industry (see Borlestean et al (2015), Skagen et al (2013) and Taboadai and R. Anadn (2016)). The Z-transform has proven itself useful in tuning LTI controlmodels for a desired control action (see Orfanidis, (2010) and Smith, (1999)) and it is on this account that its application was extended to the ecological model in pursuit of a more efficient way of estimating SR parameters to simulate an already existing output. It was however found that it could not be used for parameter tuning but rather for the extraction of the SR component hidden in the output together with components resulting from the age structure itself. Such an extraction can greatly assist in the mathematical identification of the SR, reducing the complexity of its choosing as there are many different types used in the fishing industry such as the classic Beverton-Holt model, the Ricker model and Shepherd model (Myers, 2001; Iles, 1994; Shepherd, 1982). It can also be used to monitor changes in the SR over time which can indicate the presence of strategy evolution (Apaloo et al, 2009; Br¨annstr¨om et al, 2013). In 1998 Schoombie and Getz investigated the latter by subjecting the Shepherd SR to strategy optimization with regards to a parameter associated with population interventions in regulating recruitment throughput and it is because of this versatility that the Shepherd SR is chosen for the intended extraction. In true control style, Simulink, a graphic environment for designing control simulations, is used to visualize the production of the output as well as the extraction of the SR from it. This paper showcases the versatility of the Z transform and the possibilities and unexpected finds when applied to similar systems designed to regulate signals or, in this case, recruitment densities.

Parameterized Trajectory Optimization and Tracking Control of High Altitude Parafoil Generation

Parafoil trajectory directly affects the power generation of a high-altitude wind power generation (HAWPG) device. Therefore, it is particularly important to optimize the parafoil trajectory and then to track it effectively. In this paper, the trajectory of the parafoil at high altitudes is optimized and tracked in a comprehensively parameterized manner. Both the complex dynamic characteristics of the parafoil and the dexterous demand of the high-altitude controller are considered. Firstly, the trajectory variables and control signals are parameterized as Lagrange polynomials in terms of the corresponding values at the selected nodes. Then, the Radau pseudospectral method (PSM) is employed to reformulate the original dynamic trajectory optimization problem into a static nonlinear programming (NLP) problem. By doing so, the parameterized optimal trajectory, which has the maximum net power generation, can be obtained. To attenuate the strong nonlinear, multivariable and coupling characteristics of the flexible parafoil, a bandwidth parameterized linear extended state observer (ESO) is used to estimate and reject these dynamics explicitly in a unified way. Finally, the simulation results demonstrate the effectiveness of the proposed parameterized trajectory optimization and control strategies. The main contribution of this study is that complicated nonlinear parafoil dynamics with a complex trajectory can be well regulated by a PID-type linear time-invariant controller, which is appealing for practitioners.

Reset Control of Parallel MISO Systems

The proportional–integral plus Clegg integrator (PI + CI) controller is a hybrid extension of the proportional–integral (PI) controller that is able to overcome fundamental limitations of the linear and time-invariant control systems, potentially obtaining faster responses without increasing overshooting. This work focused on the analysis and design of PI + CI controllers and reset controllers in general, for the case of parallel multiple-input single-output (MISO) systems, extending previous design methods developed for the single-input single-output (SISO) case. Several design strategies were developed: one for first-order MISO plants achieving a flat response with a finite settling time, and for second-order MISO plants obtaining a fast response with a reduced overshoot and settling time in comparison with non-hybrid strategies. Several case studies were also developed to illustrate the potential of the proposed methods.

Stable switched controllers for a swarm of UGVs for hierarchal landmark navigation

This paper presents the development of a new set of switched velocity controllers of a swarm of unmanned ground vehicles (UGVs) from multiple Lyapunov functions, which are invoked according to a switching rule. The Lyapunov-based Control Scheme (LbCS) has derived the multiple Lyapunov functions that fall under the artificial potential field method of the classical approach. Interaction of the three main pillars of LbCS, which are safety, shortness, and smoothest path for motion planning, bring about cost and time effectiveness and efficiency of the velocity controllers. The switched controllers enable the UGVs to navigate autonomously via hierarchal landmarks in a cluttered workspace to their equilibrium state. The switched controllers give rise to a switched system whose stability is proven using Branicky’s stability criteria for switched systems based on multiple Lyapunov functions. Simulations results are presented to show the effectiveness of the nonlinear time-invariant controllers. Later, effects of noise are included in the velocity controllers to show system robustness.

Design and implementation of decoupled periodic control scheme for a laboratory-based quadruple-tank process

It is well known that linear time-invariant controllers fail to provide desired robustness margins (e.g. gain margin, phase margin) for plants with non-minimum phase zeros. Attempts have been made in literature to alleviate this problem using high-frequency periodic controllers. But because of high frequency in nature, real-time implementation of these controllers is very challenging. In fact, no practical applications of such controllers for multivariable plants have been reported in literature till date. This article considers a laboratory-based, two-input–two-output, quadruple-tank process with a non-minimum phase zero for real-time implementation of the above periodic controller. To design the controller, first, a minimal pre-compensator is used to decouple the plant in open loop. Then the resulting single-input–single-output units are compensated using periodic controllers. It is shown through simulations and real-time experiments that owing to arbitrary loop-zero placement capability of periodic controllers, the above decoupled periodic control scheme provides much improved robustness against multi-channel output gain variations as compared to its linear time-invariant counterpart. It is also shown that in spite of this improved robustness, the nominal performances such as tracking and disturbance attenuation remain almost the same. A comparison with [Formula: see text]-linear time-invariant controllers is also carried out to show superiority of the proposed scheme.