Static Controller Design Research Articles

Autonomous Spacecraft Rendezvous Using Tube-Based Model Predictive Control: Design and Application

As the concentration of large space debris increases, how rendezvous maneuvers involving these typically non-cooperative, freely tumbling bodies are planned and executed is evolving. The rendezvous must be carefully planned, employing up-to-date in situ data to identify the inertial and motion parameters of the target body, and executed in a manner that accounts for the remaining uncertainty in these parameters. This paper presents an extension of the Tumbling Rendezvous via Autonomous Characterization and Execution (TRACE) pipeline used in the ROAM/TumbleDock Astrobee experiment campaign, which sequences the target state estimation, motion planning, controller design, and maneuver execution tasks while additionally providing logical loop-back avenues to previous tasks, increasing the chances of a successful maneuver. The pipeline’s performance is analyzed in simulation, utilizing target state estimates generated in a previous activity on a dedicated on-ground test bed; online motion planning, based on nonlinear programming and warm-started using a trajectory library generated offline with a novel graphics-processing-unit-based method; and tube-based model predictive control to robustly track the planned trajectory. Tube-based model predictive control is an actively evolving subject, distributed over multiple publications and various research interests. The necessary theory and considerations for practical implementation of the method are consolidated; its use, features, and limitations in the proposed task are demonstrated.

Fault Estimation and Control for Unknown Discrete-Time Systems Based on Data-Driven Parameterization Approach.

This study investigates the problem of fault estimation and control for unknown discrete-time systems. Such a problem was first formulated as an multiobjective optimization problem. Then, a data-driven parameterization controller design method was proposed to optimize both fault estimation and robust control performances. In terms of the single-objection control problem, necessary and sufficient conditions for designing the suboptimal controller were presented, and the performance index optimized by the developed data-driven method was shown to be consistent with that of the model-based method. In addition, by introducing additional slack variables into the controller design conditions, the conservatism of solving the multiobjective optimization problem was reduced. Furthermore, contrary to the existing data-driven controller design methods, the initial stable controller was not required, and the controller gain was directly parameterized by the collected state and input data in this work. Finally, the effectiveness and advantages of the proposed method are shown in the simulation results.

Robust Fixed-Order Controller Design for Uncertain Systems With Generalized Common Lyapunov Strictly Positive Realness Characterization

This article investigates the design of a robust fixed-order controller for single-input–single-output (SISO) polytopic systems with interval uncertainties, with the aim that the closed-loop stability is appropriately ensured and the performance specifications on sensitivity shaping are conformed in a specific finite frequency range. Utilizing the notion of generalized common Lyapunov strictly positive realness (CL-SPRness), the equivalence between strictly positive realness (SPRness) and strictly bounded realness (SBRness) is established; and then, the specifications on robust stability and performance are transformed into the SPRness of newly constructed systems and further characterized in the framework of linear matrix inequality (LMI) conditions. The proposed methodology avoids the tedious yet mandatory evaluations of the specifications on all vertices of the uncertain polytopic system in an explicit form. Instead, solving five LMIs exclusively suffices for ensuring the robust stability and performance regardless of the number of vertices, and thus, the typically heavy computational burden is considerably alleviated. It is also noteworthy that the proposed methodology additionally provides the necessary and sufficient conditions for this robust controller design with the consideration of a prescribed finite frequency range, and therefore, significantly less conservatism is attained in the system performance.

Virtually Euler–Lagrange form for feedback passivation of a wide range of non-Euler–Lagrange systems: Adaptive passivity-based control of hepatitis B disease

In this article, a novel technique of feedback passivation is developed for a wide range of non-Euler–Lagrange systems. The reason for this naming “Virtually Euler-Lagrange” is that it is adopted from the error dynamics of Euler–Lagrange systems. An adaptive passivity-based control strategy is proposed in virtually Euler–Lagrange form to treat hepatitis B virus infection. There are several remarkable differences between classic form of passivation and the proposed method, for example, specific and predefined template of storage function in virtually Euler–Lagrange form, which has positive definite auto-extracted form. So, it will be appropriate and time-saving for designing passivity-based control. On the contrary, the process of passivation and control design in conventional formulation is based on time-invariant input-affine systems; however, in virtually Euler–Lagrange form, the system can belong to a wider category. In this regard, two theorems have been proposed to expand the scope of passivity-based control design. Some control design conditions will be released as a result of using this new method. Furthermore, for the first time, passivity-based control has been implemented in the biological area. Control profile design, simulation results, and sensitivity analysis are carried out to evaluate capability of this control approach. Some main biological limitations are also considered, which make the proposed control more realistic.

ℋ2 reset controller design for linear systems using piecewise quadratic Lyapunov functions

SummaryThis study presents reset controller design conditions for multiple‐input and multiple‐output (MIMO) linear systems in terms of linear matrix inequalities (LMIs). The design conditions were developed using a piecewise quadratic Lyapunov function (PWQLF), leading to less conservative conditions than using a common Lyapunov function. Achieving LMI relaxation of the PWQLF‐based reset controller design conditions for MIMO linear systems is challenging because (1) dividing the flow set of the reset condition is highly complex, (2) equality constraints, which make the PWQLF continuous on the boundaries between adjacent flow sets, prevent the use of congruence transformation in matrix inequalities, and (3) indefiniteness of the matrices for regional constraints also makes it difficult to apply standard LMI relaxation techniques. To overcome these difficulties, this study introduces a two‐dimensional projection of the plant's output measurements and reset controller's states to construct a reset condition, allowing the PWQLF to be tractable in MIMO linear systems. Then, a new stability analysis condition is derived using the elimination lemma, overcoming the challenges in LMI relaxation of the controller design attributed to the equality constraints and indefinite matrices. An LMI‐based reset controller design condition is then proposed based on the proposed stability analysis. To account for transient behavior, tracking reset controller design problem is addressed. A numerical example is provided to demonstrate the effectiveness of the proposed method.

New Control Design via Switching Approach with Higher Order Derivatives of Lyapunov Function for Takagi-Sugeno Fuzzy Systems

This paper proposes a new control design method via two techniques to decrease the conservativeness in control design conditions for Takagi-Sugeno fuzzy systems that can represent a wide class of nonlinear systems. The first technique we employ is to use higher order derivatives of Lyapunov function that is shown to reduce the conservativeness in the literature. The second one is a switching approach that takes advantages of a property of the membership function. In this paper, we provide control design methods and their less conservative conditions based on the above-mentioned techniques. The proposed control design conditions are independent of the membership function and are written in a linear matrix inequality form. Finally, Numerical examples illustrate the effectiveness of the proposed control methods by comparing with the existing methods.

State bounding and synthesis of switched genetic regulatory networks with mixed delays and bounded disturbances

This paper investigates the problem of state bounding and controller design for switched genetic regulatory networks with mixed delays and bounded disturbances. A delay‐dependent sufficient condition containing several simple inequalities is first proposed to guarantee that the state trajectories remain inside or converge globally exponentially into a Cartesian product of two polytopes under the minimal dwell‐time constraint. Second, the reachable set estimation problem is further studied, and another reachable set estimation condition can be derived. Based on the reachable set estimation result, state‐feedback controllers are designed such that the state trajectories of the closed‐loop system are limited in a given Cartesian product of two polytopes. A numerical example is provided to verify the effectiveness of the obtained theoretical results.

Probability-Density-Dependent Load Frequency Control of Power Systems With Random Delays and Cyber-Attacks via Circuital Implementation

This paper studies the decentralized <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> secure load frequency control issue and circuital realization of multi-area networked power systems subject to random transmission delays and deception attacks. To make full use of the stochastic feature of the network-induced transmission delay, its distribution described by the probability density function is utilized. Due to this feature, the normal control signal and the injected deceptive attack signal transmitted over the network can be formed as two distributed delay terms. Then, the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$i$ </tex-math></inline-formula> th load frequency control area is established as a new distributed delay system, in which the delay probability density is treated as the distributed kernel. By utilizing an integral inequality dependent on the kernel, new sufficient controller design conditions are derived to guarantee the system stability with given <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> performance. Moreover, a physical execution approach is addressed to transfer the load frequency control systems into electrical analogy circuits. The effectiveness of the proposed approach is illustrated via the professional simcape toolbox in Simulink/MATLAB for circuit simulations.

Nonlinear State Observer and Control Design for Triangular Tethered Satellite Formation

This article researches the control of triangular tethered satellite formation (TTSF) system and nonlinear state observer (NSO) design when velocity vector is unmeasured. First, the stability around the equilibrium of open-loop system is discussed, which is stable around certain equilibrium pairs. To improve the system performance, linear feedback control is designed using Jacobian matrix of original nonlinear system, which is locally stable around linearized point. Besides, nonlinear control is designed subsequently which owns global stability domain. Then in case of the unmeasured velocity states, NSO is designed which contains a nonlinear function of estimation error to regulate the observation bias. With the designed nonlinear control and NSO, the simulation of the deployment of TTSF is made thereafter. Compared with linear feedback control and general observer with linear regulation, the proposed nonlinear control together with NSO has global stability domain and less chattering, which is promising in practical application.

Fixed-time synchronization of networked uncertain Euler–Lagrange systems

This paper considers the fixed-time control problem of a multi-agent system composed of a class of Euler–Lagrange dynamics with parametric uncertainty and a dynamic leader under a directed communication network. A distributed fixed-time observer is first proposed to estimate the desired trajectory and then a fixed-time robust controller is constructed by transforming uncertain Euler–Lagrange systems into second-order systems and utilizing the backstepping design procedure. The overall design guarantees that the synchronization errors converge to zero in a fixed time independent of initial conditions. The control design conditions can also be relaxed for a weaker finite-time control requirement.

Adaptive Memory-Event-Triggered Static Output Control of T–S Fuzzy Wind Turbine Systems

This article studies the weighted memory-event-triggered <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> static output control issue of Takagi–Sugeno fuzzy wind turbine systems with uncertainty. To decrease the frequency of data communication, a novel adaptive memory-event-triggered mechanism is presented to choose the “necessary” control signals, which has the following two benefits. First, a weighted average signal over a historic period is utilized as the input of event-triggered scheme, instead of the current system information in the conventional one. This could reduce the control signal updating rate and avoid the false triggering events incurred by stochastic environment noises and disturbances. Second, a dynamic triggering threshold is adopted to adaptively regulate the control signal updating frequency along with the average signal. By applying the distributed delay system method to describe the weighted historic signal, a new uncertain T–S fuzzy wind turbine system with distributed delay is established. With the aid of the measured outputs and the integral inequality based on the weighting function of the average signal, the memory-event-triggered static output controller design conditions are obtained to ensure the system exponential stability and the <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> performance. Lastly, an experiment platform integrating Zigbee modules as the wireless network is set up to illustrate the advantages of the proposed strategy.

Admissibility and admissibilization for T–S fuzzy descriptor systems with partially unknown membership functions

In this paper, the admissibility analysis and controller design issues for a class of nonlinear descriptor systems described by the T–S descriptor fuzzy model with partially unknown membership functions are discussed. New sufficient conditions are first given to ensure the admissibility of such fuzzy descriptor systems. To fully utilise the information of membership functions, the known and unknown parts of membership functions are handled by staircase functions and the bounds of the unknown part, respectively. Different from the traditional parallel distribution compensation (PDC) method, the state-feedback controller design condition is given under an imperfect premise matching method via linear matrix inequalities (LMIs). Some examples are given to show the validity of the proposed methods.

State bounding and controller design for genetic regulatory networks with multiple delays and bounded disturbances

AbstractThis article addresses the problems of state bounding and state‐feedback controller design for genetic regulatory networks with multiple delays and bounded disturbances. Multiple time‐varying discrete delays and multiple constant distributed delays are involved. A delay‐dependent sufficient condition containing several simple inequalities is first given to guarantee that the state trajectories remain inside or converge exponentially into a Cartesian product of two polytopes. Furthermore, equivalent sufficient conditions directly represented by the system parameters are derived. Based on the state bounding results, one can obtain reachable set estimation and global exponential stability criteria. By designing state‐feedback controllers, the state trajectories of the close‐loop system are limited in a given Cartesian product of two polytopes. It is worthy to stress that the proposed method does not need to construct any Lyapunov–Krasovskii functional, and it can be easily realized. The effectiveness of the obtained theoretical results is illustrated by a numerical example.

Output feedback stabilization of large-scale networked cyberphysical systems using cryptographic techniques

This paper aims to create a secure environment for state estimation and control design of a networked system composed of multiple dynamic entities and remote computational units, in the presence of disclosure attacks. In particular, both dynamic entities and computational units may be vulnerable to attacks and become malicious. The objective is to ensure that the input and output data of the benign entities are protected from the malicious parties as well as protected when they are transmitted over the network in a distributed environment. We propose a methodology integrating a novel double-layer cryptographic technique with an observer-based control algorithm to achieve the objective where the cryptographic technique addresses the security requirements and the control algorithm satisfies the performance requirements.

Relaxed stability analysis and sampled-data controller design for networked control systems with network-induced delays

This paper is devoted to the stability analysis and sampled-data controller design problem for networked control systems subject to network-induced delays. The objective is to provide relaxed conditions in terms of linear matrix inequalities. Indeed, reducing the conservatism of such conditions allows to maximize the admissible range of the network-induced delays. To do so, an augmented Lyapunov–Krasovskii functional is proposed, which involves a novel augmented state vector to include as much as possible the information from the time-varying network-induced delay into the stability conditions, together with the use of extended Wirtinger-based inequalities, an extended reciprocal convexity approach and the Finsler’s lemma. Then, declined from the proposed stability conditions, new relaxed delay-dependent conditions for the design of networked sampled-data controllers are proposed. These allow to obtain simultaneously the controller gains and the maximal allowable bound of the network-induced delays with regards to its lower bound. Three illustrative examples are provided to show the effectiveness of the proposed networked control systems stability and controller design conditions, as well as to highlight the so raised conservatism improvements regarding the previous relevant results from the literature.

Improved ℋ2 and ℒ2 control designs for discrete-time LPV/LFR systems

This paper addresses novel and norm-based controller designs for discrete-time linear parameter-varying (LPV) systems with linear fractional representation (LFR). Despite the importance of LPV/LFR systems to the control literature, there is a lack of works on this topic. The distinctive formulation of the proposed controller designs is given by using parameter-dependent Lyapunov functions in combination with slack variables and general full-block multipliers. Such proposed formulation leads to less conservative synthesis conditions characterised in terms of a finite number of linear matrix inequalities for both state-feedback and static output-feedback controllers subject to and performances for discrete-time LPV/LFR systems. Improvements obtained by the proposed controller design conditions over existing methods in the area are assessed by numerical examples.

Differential algebraic observer-based trajectory tracking for parallel robots via linear matrix inequalities

This paper develops a novel observer-based trajectory tracking technique for parallel robots, modelled as differential algebraic equations, which assumes that only positions are available for control purposes while joint velocities should be estimated. Based on the direct Lyapunov method and a recently appeared factorisation for expressions in the differential mean value theorem, convex modelling and Finsler's lemma are combined to incorporate restrictions into the analysis. Two generalisations are thus achieved: the inner-loop feedback is allowed to use velocity estimates instead of the real values and the outer-loop feedback becomes fully nonlinear while taking into account the parallel characteristics of mechanisms. Moreover, both the observer and the controller design conditions are linear matrix inequalities, which can be efficiently solved via commercially available software. Illustrative examples are provided that show the advantages of the proposal against former works on the subject.

Comments on ‘Less conservative conditions for robust LQR-state-derivative controller design: an LMI approach’ and new sufficient LMI conditions for invertibility of a convex combination of matrices

This note is concerned with conditions on a set of non-singular matrices , , so that any convex combination of these matrices is also non-singular. The first part of the note points out that Theorem 2.3 in a previous paper [Beteto et al. (2021). Less conservative conditions for robust LQR-state derivative controller design: An LMI approach. International Journal of Systems Science] provides only necessary conditions, which are not sufficient in the general case. In the second part, some stability results based on Linear Matrix Inequalities (LMIs) for a class of fractional order systems are used to establish new sufficient conditions. Numerical examples are presented for illustration. The results suggest that the new LMI conditions may be less conservative compared to a test proposed in the literature on P-matrices, and also to a positive-definiteness test based on matrix cross-products.

Exponential Stabilization of LPV Systems Under Magnitude and Rate Saturating Actuators

We propose a new convex linear parameter varying (LPV) controller design conditions that regionally stabilize LPV discrete-time systems under magnitude and rate saturating actuators. Moreover, the closed-loop system has an ensured exponential stability performance. The design conditions provide regional stabilization in the sense of polyquadratic stability, allowing an estimate of the region of initial conditions yielding trajectories with guaranteed convergence to the origin. A nonlinear first-order model models the magnitude and rate saturation of the actuators. Additionally, we propose a convex optimization procedure to enlarge the estimate of the region of attraction. Our approach is used in real-time nonlinear level control, illustrating the potentialities of the practical application of the method.

On the principle of impedance-matching for underactuated wave energy harvesting systems

In recent years, the fundamental principle of impedance-matching (IM) has inspired a number of sophisticated, yet simple, control solutions for wave energy converters (WEC). Such controllers have the capability of maximising energy absorption from incoming waves with mild computational requirements, being often intuitive in their design, hence especially appealing for real-time industrial applications. Nonetheless, these control solutions are, to date, almost exclusively developed for single degree-of-freedom (DoF) (and hence fully actuated) WEC systems, hindering their application to realistic underactuated multi-DoF devices, i.e. harvesting systems where energy is extracted from only a handful of its total set of modes of motion. Motivated by this, we present, in this paper, a comprehensive derivation and discussion of the IM conditions for maximum energy absorption in underactuated multi-DoF WEC systems. In particular, we show that the IM principle for single-DoF devices can be effectively extended to underactuated multi-DoF systems, and that a set of optimality conditions can be explicitly derived. In addition, we discuss both the impact and use of this set of optimal conditions for control design and synthesis, hence effectively taking a fundamental step towards the general extension of current IM-based techniques to the case of underactuated multi-DoF devices.