Optimal Feedback Control Research Articles

Slow Decay and Turnpike for Infinite-Horizon Hyperbolic Linear Quadratic Problems

This paper is devoted to analyzing the explicit slow decay rate and turnpike in infinite-horizon linear quadratic optimal control problems for hyperbolic systems. Under suitable weak observability or controllability conditions, lower and upper bounds of the corresponding algebraic Riccati operator are proved. Then based on these two bounds, the explicit slow decay rate of the closed-loop system with Riccati-based optimal feedback control is obtained. The averaged turnpike property for this problem is also further discussed. We then apply these results to LQ optimal control problems constrained to networks of one-dimensional wave equations and also some multidimensional ones with local controls which lack a geometric control condition.

On the Accuracy of the Model Predictive Control Method

The paper investigates the accuracy of the model predictive control (MPC) method for finding on-line approximate optimal feedback control for Bolza-type problems on a fixed finite horizon. The predictions for the dynamics, the state measurements, and the solution of the auxiliary open-loop control problems that appear at every step of the MPC method may be inaccurate. The main result provides an error estimate of the MPC-generated solution compared with the optimal open-loop solution of the “ideal” problem, where all predictions and measurements are exact. The technique of proving the estimate involves an extension of the notion of strong metric subregularity of set-valued maps and utilization of a specific new metric in the control space, which makes the proof nonstandard. The result is specialized for two problem classes: coercive problems and affine problems.

Active hybrid journal bearings with lubrication control: Towards machine learning

The study proposes an approach for simulating and designing rotating machines with water lubricated active hybrid journal bearings with the load capacity is created by combination of hydrostatic and hydrodynamic effects. Lubricant supply pressure in the bearing is adjusted in each feeding channel by a controlled servovalve. Adjustable hydrostatic forces in the bearing influence the journal position and allow reject various disturbances in the system. The ANN-based model of the rotor-bearing system was used to synthesise different types of optimal feedback controllers of the rotor position. The advanced solution of the control tasks is a machine learning based model predictive controller that has considerable robustness margins under realistic operating conditions of noisy signals and uncertainties compared with the tested PID and LQG controllers. Also an approach to reduction the energy consumption in such bearings is offered by driving the system into the optimal state where the viscous friction torque is minimal. The presence and attainability of such a state are confirmed by the results of theoretical calculations and experiment.

Beyond task-space exploration: On the role of variance for motor control and learning.

This conceptual analysis on the role of variance for motor control and learning should be taken as a call to: (a) overcome the classic motor-action controversy by identifying converging lines and mutual synergies in the explanation of motor behavior phenomena, and (b) design more empirical research on low-level operational aspects of motor behavior rather than on high-level theoretical terms. Throughout the paper, claim (a) is exemplified by deploying the well-accepted task-space landscape metaphor. This approach provides an illustration not only of a dynamical sensorimotor system but also of a structure of internal forward models, as they are used in more cognitively rooted frameworks such as the theory of optimal feedback control. Claim (b) is put into practice by, mainly theoretically, substantiating a number of predictions for the role of variance in motor control and learning that can be derived from a convergent perspective. From this standpoint, it becomes obvious that variance is neither generally “good” nor generally “bad” for sensorimotor learning. Rather, the predictions derived suggest that specific forms of variance cause specific changes on permanent performance. In this endeavor, Newell’s concept of task-space exploration is identified as a fundamental learning mechanism. Beyond, we highlight further predictions regarding the optimal use of variance for learning from a converging view. These predictions regard, on the one hand, additional learning mechanisms based on the task-space landscape metaphor—namely task-space formation, task-space differentiation and task-space (de-)composition—and, on the other hand, mechanisms of meta-learning that refer to handling noise as well as learning-to-learn and learning-to-adapt. Due to the character of a conceptual-analysis paper, we grant ourselves the right to be highly speculative on some issues. Thus, we would like readers to see our call mainly as an effort to stimulate both a meta-theoretical discussion on chances for convergence between classically separated lines of thought and, on an empirical level, future research on the role of variance in motor control and learning.

Indefinite linear quadratic optimal control for discrete time‐varying linear rectangular descriptor systems

AbstractIn this article, the indefinite linear quadratic (LQ) optimal control problem for discrete time‐varying rectangular descriptor systems is investigated, in which the indefinite weight matrices are considered in the quadratic cost function. With a suite of equivalent transformations, the indefinite LQ problem for discrete time‐varying rectangular descriptor systems can be substituted by an equivalent indefinite LQ problem for standard state space systems. Then, the transformed equivalent indefinite LQ problem is solved by establishing a dual Krein space model, and the optimal control and optimal cost value are obtained by invoking the Kalman filter of Krein space. The form of state feedback optimal control corresponding to the original system is given. Next, to guarantee the dynamic part for the resulting optimal closed‐loop system has a unique solution, some necessary and sufficient conditions are proposed. Finally, a numerical example is carried out to demonstrate the availability of established results.

Insight into the hierarchical control governing leg stiffness during the stance phase of running

Leg stiffness plays a key role in the storage and release of elastic energy during stance. However, the extent to which a runner is able to reuse stored energy remains a limiting factor in determining their running effectiveness. In this study, ten habitual rearfoot strikers and ten habitual forefoot strikers were asked to run on a treadmill in three footwear conditions: traditional, neutral, and minimal running shoes. We examined the effect of habitual foot strike pattern and footwear on leg stiffness control within three task-relevant phases of stance (i.e. touch-down, loading, unloading). Control was quantified using stride-to-stride leg stiffness time-series and the coefficient of variability and detrended fluctuation analysis (DFA). The results are interpreted within a theoretical framework that blends dynamic systems theory and optimal feedback control. Results indicate that leg stiffness control is tightly regulated by an active control process during the loading period of stance. In contrast, the touch-down and unloading phases are driven mostly by passive allometric control mechanisms. The effect of footwear on leg stiffness control was inconclusive due to inconsistent trends across three shoe types. However, stiffness control was affected by landing technique. Habitual rearfoot strike runners have reduced DFA values during the touch-down and unloading phases. These sub-phases are associated with an allometric control process and suggests that rearfoot strike runners express a reduction in system complexity for leg stiffness control and hence, a less adaptable system.

Model Predictive Regulation on Manifolds in Euclidean Space.

One of the crucial problems in control theory is the tracking of exogenous signals by controlled systems. In general, such exogenous signals are generated by exosystems. These tracking problems are formulated as optimal regulation problems for designing optimal tracking control laws. For such a class of optimal regulation problems, we derive a reduced set of novel Francis–Byrnes–Isidori partial differential equations that achieve output regulation asymptotically and are computationally efficient. Moreover, the optimal regulation for systems on Euclidean space is generalized to systems on manifolds. In the proposed technique, the system dynamics on manifolds is stably embedded into Euclidean space, and an optimal feedback control law is designed by employing well studied, output regulation techniques in Euclidean space. The proposed technique is demonstrated with two representative examples: The quadcopter tracking control and the rigid body tracking control. It is concluded from the numerical studies that the proposed technique achieves output regulation asymptotically in contrast to classical approaches.

Optimal negative derivative feedback controller design for collocated systems based on [formula omitted] and [formula omitted] method

In this paper, a direct procedure is presented in order to design negative derivative feedback (NDF) controller for collocated systems. Collocated systems have embedded sensors and actuators, which have an alternating poles and zeroes in frequency domain, which creates asymptotic stability. NDF is a band-pass filter, cutting off the control action far from the natural frequencies associated with the controlled modes, which reduces the spillover effect. Since it is a band-pass filter, it can effectively control the lower and higher frequency disturbances. Also, it is very efficient controller for higher frequencies’ vibration mitigation. An approach for an optimal design of NDF controller to implement on collocated system is presented. A simple, collocated system is considered and a mode of it is targeted to damp. Maximum damping method is used to extract all of the controller constants dependent on closed-loop damping value. Afterward, H2 and H∞ methods are utilized to determine the closed-loop damping value optimally. The results show that NDF not only can easily damp the targeted mode impactfully but also can reduce some level of vibrations in the modes after that as well. This shows the power of NDF filter on vibration mitigation of modes located in a band of frequency. The proposed method is applicable for any general system and for any zero/pole patterns of collocated system, easily. It can be applied for any collocated system with zero before pole pattern or zero after pole pattern.

Constrained Decoupling Adaptive Dynamic Programming for A Partially Uncontrollable Time-Delayed Model of Energy Systems

The lack of feedback-loop design and uncontrollable state reconstruction, such as load demand and renewable generation, are key factors to hinder the development of energy control. Adaptive dynamic programming is an efficient method to break through the bottleneck. However, most current works assume that the evolution of uncontrollable state satisfies Markovian property. This paper proposes a time-delayed adaptive dynamic programming framework for optimal energy control, utilizing more comprehensive historical data for state reconstruction. The uncontrollable state is reconstructed by an attention mechanism-based Transformer network based on online measured data. Then, a self-learning iterative algorithm is developed to obtain the optimal state feedback control policy under a discounted performance index function. The problem of solving iterative control policy, which is a mixed-integer nonlinear programming problem with an enormous computational burden, is decomposed into three sub-problems, i.e. nonlinear programming with no discrete variable, which is solved by the Projected Newton method, mixed-integer quadratic programming, and quadratic programming. Numerical results illustrate that the developed control algorithm minimizes the electricity cost in the long term and avoids peak load.

Optimal adaptive state feedback control for a three degree-of-freedom series-type double inverted pendulum system by using particle swarm optimisation

ABSTRACT This research tries to stabilise a three degree-of-freedom series-type double inverted pendulum system by employing an adaptive state feedback control approach optimised by a particle swarm optimisation (PSO) algorithm. To this end, the dynamical equations are derived via Lagrangian method and linearised by utilising approximation approaches. Then, the state feedback scheme is implemented to control the system states, that is, the angle and angular velocity of the first and second poles as well as the position and velocity of the cart. In order to timely regulate the control gains, the adaptation rules based on the gradient descent method and sliding surface relations are applied. The particle swarm optimisation algorithm is implemented to optimally tune the design parameters of the controller based on a proper objective function defined as summation of integrals of absolute values of the system errors. The time responses of the angles of the poles and the position of the cart clearly depict the feasibility and efficiency of the introduced control strategy to stabilise the system from different initial conditions to the final desired values.

Optimal Linear Quadratic Control for Knee-Ankle Orthosis System

The control technique for an exoskeleton system for lower limb rehabilitation is complicated, and numerous internal and external elements must be taken into account, in addition to the uncertainties in the system model. In this paper, through the analysis of the lower extremity exoskeleton is utilized to obtain the corresponding equation and its linearized form. The nonlinear differential equations have been linearized by using Jacobean’s method in order to facilitate the controller design. Considering the interior and external factors of the connecting rod, the uncertain elements are introduced and therefore the optimal control technique is applied to regulate the system. An optimal state feedback control strategy of Linear Quadratic Regulator (LQR), and LQR-Servo have been implemented in this work. Finally, the physical parameters of the Knee-Ankle Orthosis (KAO) exoskeleton are used, and the simulation results show the advantage and applicability of the proposed controller’s design of the Knee-Ankle orthosis system. Index Terms— Rehabilitation, Knee-Ankle orthosis (KAO), Optimal control, LQR-Servo controller.

Development of Machine Learning Based Control System for Vehicle Active Suspension System

In this paper, Gaussian process (GP) algorithm, which is one of the machine learning methods, is designed to control the vehicle active suspension system (VASS). Experimental data were trained by supervised learning method (regression method). The data were obtained from an optimal linear quadratic controller tuned based on a full state feedback optimal control approach. The results demonstrated that the proposed machine learning (ML) based ground-penetrating radar (GPR) controller outperforms the optimal controller under uncertainties in terms of reducing the oscillation in sprung mass position with a 15% and 21.64% reduction for square and random road conditions, respectively.

Scheduling and control of high throughput screening systems with uncertainties and disturbances

ABSTRACT Based on the existing research work on the modeling and control of cyclically operated high-throughput screening systems, this paper presents the scheduling and control of high-throughput screening systems with uncertainties and disturbances. Different definitions of disturbance decoupling problems are considered in order to achieve the optimal scheduling of high-throughput screening systems. Online scheduling was achieved by computing optimal prefilters and output feedback controllers, which can be computed using residuation theory. The control strategies achieved by the controllers are optimal in the sense of the just-in-time criterion commonly used in industrial schedule practice.

Data-driven adaptive-critic optimal output regulation towards water level control of boiler-turbine systems

This paper considers a new adaptive-critic optimal output regulation scheme for continuous-time general linear systems with unknown dynamics and unmeasurable disturbance. The objective of researching the optimal output regulation problem is pursuing the stability of the closed-loop system while enabling the output to optimally track the reference signal with disturbance rejection. The problem is solved by employing an approximate optimal regulator that consist of optimal feedback control obtained by a data-driven learning algorithm and optimal feedforward control achieved by solving regulator equation. The missing system matrices of the plant are exactly figured out by employing state/input data. Moreover, by employing the minimal polynomial of the exosystem matrix, the parameter of interference in the output equation is available. Then, a predefined cost function is presented based on the regulator equation that aims to design the optimal control law. The stability analysis demonstrate that the presented control scheme can stabilize the closed-loop system, meanwhile the output asymptotically tracks the reference signal. Finally, the effectiveness of the developed optimal control scheme is validated through an application towards the drum water level control of boiler-turbine systems.

Robust decentralized optimal stabilizability of continuous time uncertain interconnected systems: Application to large scale power system

This article introduces a new design of a decentralized robust optimal feedback controller for a class of large-scale systems using the modified algebraic Riccati equations. The studied class of large-scale systems is characterized by structured uncertainties that are bounded. Our main contribution in this work is the use of the Lyapunov direct method for the stability analysis, associated with a quadratic function, in order to determine a new sufficient condition to guarantee the global asymptotic stability of the class of the studied uncertain interconnected systems. The proposed control approach is then implemented on a large-scale power systems composed of three interconnected generators. Simulation results show that the proposed robust optimal controller is quite effective and has an outstanding performance.

A self-sensing and self-actuating metamaterial sandwich structure for the low-frequency vibration mitigation and isolation

Sandwich structures (SSs) are widely deployed in engineering applications, such as for the low-frequency vibration or acoustic mitigation and isolation. However, it is challenging to enhance their low-frequency vibration mitigation and isolation performance while maintaining their multi-functionalities, such as lightweight, high bending stiffness, and high impact absorption ability, etc. To achieve this objective, local resonators are introduced into a hollow-tube core lattice sandwich structure (HLSS) in this paper, which is referred to as the metamaterial sandwich structure (MMSS-1). The proposed MMSS-1 is composed of periodically distributed thin-walled hollow tubes with attached resonators as the core, and two thin cover-plates or face-sheets. The band structures and the corresponding eigenmodes of the unit-cell of the MMSS show that both the Bragg scattering and the local resonance band-gaps coexist in the proposed MMSS-1. The influences of the key geometrical and material parameters of the MMSS-1 on the band-gaps are analyzed in details. Then, the piezoelectric patches are attached to the top and bottom face-plate surfaces of the MMSS-1 and resonators to form the MMSS-2, and they are shunted via an active feedback control to build the MMSS-3. The effects of the displacement feedback control gains on the band-gaps of the MMSS-3 are studied. Based on the active displacement feedback control and differential evolution (DE) optimization algorithm, a self-sensing and self-actuating strategy is developed to lend the self-adaptive capability to the MMSS-3, which is referred to as the self-adaptive MMSS. The vibration or flexural wave propagation in the finite-sized self-adaptive MMSS is numerically simulated to demonstrate its outstanding ability for low-frequency vibration mitigation and isolation. It shows that the proposed self-adaptive MMSS can evolve different control parameters automatically to widen and merge Bragg scattering band-gaps and local resonance band-gaps without human intervention. In addition, the vibration attenuation inside the band-gaps is also enhanced. The proposed self-sensing and self-actuating strategy can improve the vibration mitigation and isolation performance of the HLSSs significantly in the low-frequency range. The proposed self-adaptive MMSS may pave a novel and feasible way for the design and applications of the HLSSs for the low-frequency vibration mitigation and isolation in civil engineering, mechanical engineering, and aerospace engineering etc. Moreover, the proposed self-adaptive strategy via self-sensing and self-actuating can be also applied to other types of the SSs for improving their vibration mitigation and isolation performance, and for the NVH (noise, vibration and harshness) of vehicles, high-end equipment and high-precision instruments.

Self-triggered control of probabilistic Boolean control networks: A reinforcement learning approach

In this work, strategies to devise an optimal feedback control of probabilistic Boolean control networks (PBCNs) are discussed. Reinforcement learning (RL) based control is explored in order to minimize model design efforts and regulate PBCNs with high complexities. A Q-learning random forest (QLRF) algorithm is proposed; by making use of the algorithm, state feedback controllers are designed to stabilize the PBCNs at a given equilibrium point. Further, by adopting QLRF stabilized closed-loop PBCNs, a Lyapunov function is defined, and a method to construct the same is presented. By utilizing such Lyapunov functions, a novel self-triggered control (STC) strategy is proposed, whereby the controller is recomputed according to a triggering schedule, resulting in an optimal control strategy while retaining the closed-loop PBCN stability. Finally, the results are verified using computer simulations.

Bilinear Control of Convection-Cooling: From Open-Loop to Closed-Loop

This paper is concerned with a bilinear control problem for enhancing convection-cooling via an incompressible velocity field. Both optimal open-loop control and closed-loop feedback control designs are addressed. First and second order optimality conditions for characterizing the optimal solution are discussed. In particular, the method of instantaneous control is applied to establish the feedback laws. Moreover, the construction of feedback laws is also investigated by directly utilizing the optimality system with appropriate numerical discretization schemes. Computationally, it is much easier to implement the closed-loop feedback control than the optimal open-loop control, as the latter requires to solve the state equations forward in time, coupled with the adjoint equations backward in time together with a nonlinear optimality condition. Rigorous analysis and numerical experiments are presented to demonstrate our ideas and validate the efficacy of the control designs.

Optimal feedback control for a class of fractional evolution equations with history-dependent operators

In this paper, we will study optimal feedback control problems derived by a class of Riemann-Liouville fractional evolution equations with history-dependent operators in separable reflexive Banach spaces. We firstly introduce suitable hypotheses to prove the existence and uniqueness of mild solutions for this kind of Riemann-Liouville fractional evolution equations with history-dependent operators. Then, by introducing a feedback iterative technique and applying Filippov theorem, we show the existence of feasible pairs and optimal control pairs of the optimal feedback control systems with history-dependent operators. Finally, we give some applications to illustrate our main results.

Uniqueness of the Riccati operator of the non-standard ARE of a third order dynamics with boundary control

Abstract The Moore-Gibson-Thompson [MGT] dynamics is considered. This third order in time evolution arises within the context of acoustic wave propagation with applications in high frequency ultrasound technology. The optimal boundary feedback control is constructed in order to have on-line regulation. The above requires wellposedness of the associated Algebraic Riccati Equation. The paper by Lasiecka and Triggiani (2022) recently contributed a comprehensive study of the Optimal Control Problem for the MGT-third order dynamics with boundary control, over an infinite time-horizon. A critical missing point in such a study is the issue of uniqueness (within a specific class) of the corresponding highly non-standard Algebraic Riccati Equation. The present note resolves this problem in the positive, thus completing the study of Lasiecka and Triggiani (2022) with the final goal of having on line feedback control, which is also optimal.