Control Of Discrete-time Linear Systems Research Articles

Distributed Optimal Control of Discrete-Time Linear Systems Over Networks

Distributed Optimal Control of Discrete-Time Linear Systems Over Networks

Singularity-free adaptive control of discrete-time linear systems without prior knowledge of the high-frequency gain

This paper proposes a new output feedback model reference adaptive control (MRAC) method for discrete-time linear time-invariant systems with arbitrary relative degrees. The proposed method does not require any prior knowledge of the high-frequency gain represented by kp, thereby completely eliminating the common design condition in the traditional discrete-time MRAC framework: the sign of kp is known, as well as an upper bound on |kp|. Specifically, an output feedback adaptive control law is developed, which incorporates a time-varying gain function to effectively address the singularity issue. The developed adaptive control law leads to the derivation of a linear estimation error equation for the closed-loop system. Consequently, a gradient algorithm based parameter update law is directly formulated by utilizing the estimation error and some other available signals without requiring any prior knowledge of kp. In comparison to the traditional MRAC and Nussbaum function-based methods, it does not necessitate any additional design conditions or involve any transient performance issues, while still ensuring closed-loop stability and asymptotic output tracking for any given bounded reference signal. The simulation study showcases the design procedure and evaluates the efficacy of the proposed control method.

Self-triggered robust output feedback model predictive control of discrete-time linear systems

In networked control systems, the communication load is a main concern for implementing model predictive control (MPC). This paper introduces a self-triggered MPC algorithm under network environments to reduce communication load, for discrete-time linear systems with bounded state and output disturbances, when only the system output can be measured at triggering instants. The proposed algorithm mainly based on a state estimator whose estimation error is bounded by an invariant set, and on the self-triggered model predictive control of a nominal system. Moreover, the new cost function explicitly adopts communication load is in consideration. The proposed algorithm is proved to drive the system to an invariant set with respect to the bounded disturbances. Finally, simulation results is provided to verify the effectiveness of the proposed robust output feedback MPC algorithm.

Construction of the Time-Optimal Bounded Control for Linear Discrete-Time Systems Based on the Method of Superellipsoidal Approximation

Construction of the Time-Optimal Bounded Control for Linear Discrete-Time Systems Based on the Method of Superellipsoidal Approximation

Model predictive control of discrete-time linear systems by ADMM with applications to turbofan engine control problems

Model predictive control of discrete-time linear systems by ADMM with applications to turbofan engine control problems

Limitations of energy SNR in control over channels with and without feedback

This paper presents limitations of energy signal-to-noise ratio (SNR) in control of discrete-time linear systems over noisy channels with and without feedback. The minimum SNR required for stabilization is shown to be the modulus of the product of unstable poles of the plants. Two types of optimal control laws that achieve this minimum are constructed based on the gains for expensive control, that is, LQ optimal control without input weight. It is observed that channel feedback does not improve the SNR limitation, which means feedback for control is efficient enough for communication.

Average dwell time based networked predictive control for switched linear systems with data transmission time-varying delays

Abstract This paper investigates an average dwell time (ADT) based networked predictive control for discrete-time linear systems with data transmission time-varying delays. Since the data transmission time-varying delays and packet dropouts simultaneously exhibit in the sensor-to-controller and the controller-to-actuator channels, a predictor is proposed to approximate the current state with the delayed state measurement. Based on the estimation state, a synchronous switching controller is proposed, and its mode-dependent and mode-independent design methods are presented. The proposed methods not only guarantee the desired stability of the closed-loop systems but also tolerate some locally unstable subsystems. In addition, the decay rate of the closed-loop system can be pre-regulated. Moreover, given some prior activation probabilities of subsystems, the ADT can be further reduced, thus more frequent switching dynamics can be allowed. Numerical example is provided to show the effectiveness of the developed method.

Robust Model Predictive Control Using a Two-Step Triggering Scheme

This article is concerned with event-triggered robust model predictive control for linear discrete-time systems with bounded disturbances. A two-step scheme involving a tentative verification of a triggering condition and a delayed triggering with a waiting horizon is proposed to reduce the average triggering rate and fully utilize the nominal optimal control sequence minimizing a quadratic cost function. The triggering condition and the waiting horizon are synthesized based on a prediction model of the plant and a robust positively invariant set associated with it. Under mild conditions, recursive feasibility and closed-loop robust stability are guaranteed. Two examples are used to show the effectiveness and merits of the proposed approach.

H₂ Performance Analysis and Synthesis for Discrete-Time Linear Systems With Dynamics Determined by an i.i.d. Process

This letter is concerned with <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${H}_{2}$ </tex-math></inline-formula> control of discrete-time linear systems with dynamics determined by an independent and identically distributed (i.i.d.) process. A definition of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${H}_{2}$ </tex-math></inline-formula> norm is first discussed for the class of systems. Then, a linear matrix inequality (LMI) condition is derived for the associated performance analysis, which is tractable in the sense of numerical computation. The results about analysis are also extended toward state-feedback controller synthesis.

On the Design of Robust Four Degree of Freedom Controllers for Linear Discrete-Time Systems

On the Design of Robust Four Degree of Freedom Controllers for Linear Discrete-Time Systems

Design of Fractional Order Odd-Harmonics Repetitive Controller for Discrete-Time Linear Systems with Experimental Validations.

This paper presents a simple and straightforward design of a discrete-time fractional-order odd-harmonics repetitive controller (RC). Unlike general RC designs, the proposed method utilizes an internal model with a half-period delay and a stabilizing controller with a fractional phase lead compensator. First, the odd-harmonics internal model representing odd-harmonics frequencies is constructed by using the information of the reference's basis period and the preferred tracking bandwidth. Secondly, an optimization problem synthesized from the stability condition of the RC closed-loop system is solved to obtain the fractional phase lead compensator. Finally, the fractional term of the stabilizing controller is realized by using a causal and stable infinite impulse response (IIR) filter, where the filter coefficients are computed by applying the Thiran formula. Simulation and experimental validation on a servomotor system are conducted to verify the effectiveness of the proposed design.

Model-free finite-horizon optimal tracking control of discrete-time linear systems

Conventionally, the finite-horizon linear quadratic tracking (FHLQT) problem relies on solving the time-varying Riccati equations and the time-varying non-causal difference equations as the system dynamics is known. In this paper, with unknown system dynamics being considered, a Q-function-based model-free method is developed to solve the FHLQT problem. First, an augmented system consisting of the controlled system and the desired trajectory system is formulated, and the FHLQT problem transforms to the finite-horizon linear quadratic regulator (FHLQR) problem with the augmented system. Then, a time-varying Q-function which depends explicitly on the control input is defined. With the defined time-varying Q-function, a model-free finite-horizon control method is developed to approximate the solutions of the time-varying Riccati equations of the transformed FHLQR problem. At last, simulation studies are carried out to verify the validity of the developed method.

Optimal output tracking control of linear discrete-time systems with unknown dynamics by adaptive dynamic programming and output feedback

This paper discusses the output-feedback-based model-free optimal output tracking control problem of discrete-time systems with completely unknown system models under mild assumptions. The only information that allows utilisation is the system output and the reference output. To overcome these challenges, the paper aims to solve a model-free optimal output regulation problem for achieving optimal output tracking control; solving an optimal output regulation problem is equivalent to solving a linear quadratic regulation (LQR) problem and a constrained static optimisation problem. The state reconstruction is first given to represent the system state in terms of the input and output sequences. A data-driven value iteration (VI) algorithm is then proposed to iteratively approximate the solution to the discrete-time algebraic Riccati equation (ARE) of the corresponding LQR problem on the basis of input and output data. Next, based on the iterative solutions with respect to the ARE, a model-free solution is provided for the corresponding constrained static optimisation problem. Finally, an alternative reference system equivalent to the original reference system is established to avoid the requirement of having the knowledge of the reference system dynamics and the reference state. A numerical example is employed to demonstrate the effectiveness of the proposed control scheme.

An LMI Approach to Robust Iterative Learning Control for Linear Discrete-time Systems

An LMI Approach to Robust Iterative Learning Control for Linear Discrete-time Systems

Data-driven optimal tracking control of discrete-time linear systems with multiple delays via the value iteration algorithm

In this paper, the optimal tracking problem for discrete-time linear systems with multiple delays is studied without system dynamics. It is known that the total state of a system without specific dynamic characteristics is hard to be measured, unless such a system is equipped with massive sensors, which, however, may lead to an increase in cost and complexity for analysing. To deal with this problem and avoid adverse effects caused by using system state information, a new data-driven value iteration (DDVI) algorithm is proposed by considering three factors: past control inputs, system outputs, and external reference trajectories. Before the algorithm is proposed, a transformation is made to the original system according to the characteristics of the time-delay system, so that the time-delay number can be reduced or become a delay-free system. A novel data-driven state equation is derived from the historical data of the three factors, and then, it is adopted to solve the optimal control of multi-delay systems. Further results show that the proposed DDVI algorithm is convergent and the tracking error is asymptotically stable. Finally, simulations are provided to show the effectiveness of the controller.

Robust iterative learning control for linear discrete-time systems with initial state learning

This paper investigates a new sufficient robust convergence condition of iterative learning control with initial state learning in the presence of iteration-varying uncertainty for multivariable systems in the time domain. The uncertainty in system parameters may lead to divergence of the ILC algorithm. Moreover, in the basic ILC algorithm, the initial state is constant in each iteration and, consequently, always leads to a tracking error. Providing fixed learning gains over time and iteration is a significant achievement of this norm-based method. For this purpose, first, a new robust convergence condition is designed based on the iterative learning control with initial state learning algorithm, and in the next step, a semi-optimal solution is achieved for it by the imperialist competitive algorithm . Finally, the effectiveness of the proposed convergence scheme is evaluated through two numerical examples.

Minimax Q-learning design for H∞ control of linear discrete-time systems

Minimax Q-learning design for H∞ control of linear discrete-time systems

Optimized Over-the-Air Computation for Wireless Control Systems

The over-the-air controller was recently proposed to enable efficient computation of the control signal for control systems, by leveraging the over-the-air computation concept. This letter introduces a transmit power allocation scheme for the over-the-air controller, where the wireless channel directly produces the control gain of a discrete-time linear control system. The proposed design scheme essentially minimizes the worst effect of the channel noise to the desired control system output, subject to the transmit power limit over the wireless channel. Despite the non-convexity of the problem, we derive the control cost criterion as linear matrix inequalities with transmit power constraints. We comprehensively investigate the control performance and the transmit power cost of the proposed scheme in various scenarios. The proposed optimization scheme shows significant control performance gain against the state-of-the-art solution, while having a comparable transmit power consumption.

Event-Triggered Control for Discrete-Time Systems Using a Positive Systems Approach

We provide an output feedback event-triggered controller for discrete-time linear systems. We make novel use of positive systems, interval observers, an event-triggered state estimator, and triggering times that are computed from estimator values. This provides a discrete-time analog of our recent positive systems approach for continuous-time systems. A key novel ingredient in our discrete-time event triggers is their use of vectors of absolute values, instead of the usual Euclidean norm. We illustrate the benefits of our method using a model for event-triggered BlueROV2 underwater vehicles.

Stochastic model predictive control for linear systems affected by correlated disturbances

In this paper, the problem of stability, recursive feasibility and convergence conditions of stochastic model predictive control for linear discrete-time systems affected by a large class of correlated disturbances is addressed. A stochastic model predictive control that guarantees convergence, average cost bound and chance constraint satisfaction is developed. The results rely on the computation of probabilistic reachable and invariant sets using the notion of correlation bound. This control algorithm results from a tractable deterministic optimal control problem with a cost function that upper-bounds the expected quadratic cost of the predicted state trajectory and control sequence. The proposed methodology only relies on the assumption of the existence of bounds on the mean and the covariance matrices of the disturbance sequence.