Control Of Discrete-time Linear Systems Research Articles

Variable-structure repetitive control for discrete-time linear systems with multiple-period exogenous signals

Variable-structure repetitive control for discrete-time linear systems with multiple-period exogenous signals

Performance Improvement of Discrete-time Linear Control Systems Subject to Varying Sampling Rates Using the Tikhonov Regularization Method

Methods to stabilize discrete-time linear control systems subject to variable sampling rates, i.e., using state feedback controllers, are well known in the literature. Several recent works address the use of the Tikhonov regularization method, originally designed to attenuate the noise effects on ill-posed problems, with the aim of improving performance and stabilizing approximately controllable dynamical systems. Inspired by these works, we propose the use of a feedback controller designed using the Tikhonov method to regularize discrete-time linear systems subject to varying sampling rates. The goal is to minimize an error function, thus improving the performance of the closed loop system and reducing the possibility of instability. Illustrative examples show the effectiveness of the proposed method.

Hybrid Optimal LQG Tracking Control for Linear Discrete-Time Systems by Simultaneous Optimization Approach of System States and Mode Distributions

In this paper, we study optimal LQG tracking control problems for linear discrete-time hybrid systems. We adopt an approach to prepare some candidates of mode distributions and minimize value functions at each time for the systems and performance indices. By the approach, system states and mode distributions are simultaneously optimized so that performance indices are minimized for causal information of reference signals. We consider optimization problems for averaged systems and averaged performance indices throughout mode distributions. Finally, we give numerical examples and verify that we can obtain both optimal tracking performance and optimal candidate of mode distributions by the algorithm presented in this paper.

New LMI conditions for H ∞/H 2 output feedback control of linear discrete-time systems

ABSTRACT This paper addresses the design of static output feedback controller for linear discrete-time systems. New sufficient criteria are derived for designing and controllers. The corresponding design criteria are presented in the form of Linear Matrix Inequalities (LMIs). The development involves certain relaxations of the LMI variables through appropriate use of bounding inequalities leading to less conservative LMI design criteria. The proposed method is compared with existing ones through numerical examples to illustrate the effectiveness of the design method.

Constrained Control of Linear Discrete-Time Systems Under Quartic Performance Criterion

In several applications, a performance criterion that is quartic in the state can be a desired alternative to the classic quadratic control. This letter proposes a receding horizon controller for linear time-invariant systems subject to linear state and input constraints, which makes use of a running cost that is quadratic in the input and quartic in the state. Stability and recursive feasibility of the proposed receding horizon scheme are proven. Numerical simulations are presented, considering the problem of controlling a single-link inverted pendulum on a cart.

Shrinking Horizon Model Predictive Control With Signal Temporal Logic Constraints Under Stochastic Disturbances

We present shrinking horizon model predictive control for discrete-time linear systems under stochastic disturbances with constraints encoded as signal temporal logic (STL) specification. The control objective is to satisfy a given STL specification with high probability against stochastic uncertainties while maximizing the robust satisfaction of an STL specification with minimum control effort. We formulate a general solution, which does not require precise knowledge of probability distributions of (possibly dependent) stochastic disturbances; only the bounded support of the density functions and moment intervals are used. For the specific case of disturbances that are normally distributed, we optimize the controllers by utilizing knowledge of the probability distribution of the disturbance. We show that in both cases, the control law can be obtained by solving optimization problems with linear constraints at each step. We experimentally demonstrate effectiveness of this approach by synthesizing a controller for a heating, ventilation, and air conditioning system.

Estimation of the domain of attraction for discrete-time linear impulsive control systems with input saturation

This paper discusses the domain of attraction and stability analysis for discrete-time linear impulsive systems with input saturation. The first goal is to give a stable condition for the system. The second is to present a strategy to find an inner estimate of the domain of attraction via establishing Lyapunov functions and using other mathematical methods. Finally, we present several examples to illustrate the validity of the conditions we have derived.

An ADDHP-based Q-learning algorithm for optimal tracking control of linear discrete-time systems with unknown dynamics

This paper investigates a novel Q-learning algorithm based on action dependent dual heuristic programming (ADDHP) to solve the infinite-time domain linear quadratic tracker (LQT) for unknown linear discrete-time systems. The proposed method is conducted based on only system data without requiring the knowledge of the system matrices. After the reference system is determined, an augmented system composed of the original system and the reference system is constructed, and it is proved that the value function of LQT is quadratic concerning the state of the augmented system. Using the quadratic value function, the augmented algebraic Riccati equation (ARE) is derived to solve the LQT. Due to the difficulty of directly solving the augmented ARE, a Q-learning algorithm based on ADDHP structure is used to solve this problem. With unknown system matrices, a model neural network is developed to reconstruct system dynamics incorporating stability analysis. The estimated system matrices are employed to the proposed algorithm to calculate the optimal control by policy iteration. Moreover, the convergence of the algorithm is proved. Two simulation examples are used to validate the performance of the method, where all results have demonstrated the effectiveness of the proposed ADDHP-based Q-learning method without a priori knowledge of system matrices for LQT.

Robust predictive control based on the Meixner-like model

This paper is devoted to the issue of a robust predictive control for linear discrete-time systems by using Meixner-like model. The Meixner-like functions are an extension of Laguerre functions and convenient when the system has a slow start or delay. To ensure the reduction of the parameter number in the Meixner-like model, the optimization of parameters characterizing the Meixner-like functions is proposed. This proposed robust predictive control copes with physical constraints and geometrical constraints due to parameter uncertainties, which are estimated by using the Unknown But Bounded Error (UBBE) approach, and leads to the min-max optimization problem.

Kernel methods for the approximation of discrete-time linear autonomous and control systems

Methods from learning theory are used in the state space of linear dynamical and control systems in order to estimate relevant matrices and some relevant quantities such as the topological entropy. An application to stabilization via algebraic Riccati equations is included by viewing a control system as an autonomous system in an extended space of states and control inputs. Kernel methods are the main techniques used in this paper and the approach is illustrated via a series of numerical examples. The advantage of using kernel methods is that they allow to perform function approximation from data and, as illustrated in this paper, allow to approximate linear discrete-time autonomous and control systems from data.

Reliable control of discrete-time linear systems with actuator failure

A sufficient condition is given for robust stability of a discrete linear system in which an arbitrary portion of input channel is permanently attenuated or disconnected due to actuator fault. The partial disconnection/attenuation of the control input, is modelled as uncertainty and dealt with via a robust control method. The proposed method enables one to design a controller in such a way that the closed loop system remains stable when any combination of input signals is disconnected if the open loop system is stable and fulfils some additional properties. It is shown that the linear quadratic regulator can guarantee reliable closed loop with some specific choices for weighting matrices. The result is extended to unstable systems by assuming additional constraints on the failed actuators. Compared to previously established results, the proposed conditions are easier to verify and applicable to a wider class of systems. An example is also included.

Data-driven robust fault tolerant linear quadratic preview control of discrete-time linear systems with completely unknown dynamics

In this paper, we propose a data-driven robust fault tolerant preview control scheme for discrete-time LTI systems with completely unknown dynamics. In general, this work consists of three key design parts. Firstly, the Markov parameters sequence is identified to extract system feature from data. Then, robust linear quadratic preview control policy composed of finite data feedback, integral operation and preview action is designed through establishing data-space characterisation and solving the related convex optimisation problem. Thirdly, an active fault tolerant method composed of fault detection, isolation, estimation and corresponding compensation is further constructed to accommodate fault influence. Note that all these involved designs are performed at Markov parameters sequence level. Thus above integrated preview control scheme can avoid the priori knowledge requirements including system matrices, order, and state variables. The effectiveness of the obtained results is finally verified via a case study of the injection moulding machine.

Distributed Secure Filtering for Discrete-Time Systems Under Round-Robin Protocol and Deception Attacks.

This paper addresses the problem of designing a distributed filter for linear discrete-time networked control systems that suffer from randomly occurring deception attacks and bounded disturbances. A Round-Robin-type protocol is applied to schedule communication between filters due to the communication resource constraint. The discrete-time Wirtinger's inequality is used to derive a sufficient condition that ensures H∞ performance of the closed-loop system. A corresponding filter that guarantees the security is designed. Finally, a numerical example of an inverted pendulum system is provided to demonstrate the feasibility of the proposed filter.

Discrete Fourier transform based frequency characteristics of iterative learning control for linear discrete-time systems

For discrete-time iterative learning control systems, the discrete Fourier transform (DFT) is a powerful technique for frequency analysis, and Toeplitz matrices are a typical tool for the system input–output transmission. This paper first exploits z-transform and DFT-based frequency properties for iterative learning control systems and studies the convergence property of a Toeplitz matrix to the power of iteration index. The exploitation exhibits that for the finite-length discrete-time iterative learning control systems, the time-domain convolution theorem for the z-transform and DFT is no longer true, and the Toeplitz matrix to the power of iteration index converges if and only if the identical diagonal element lies in the unit circle. Then, by considering the DFT to a finite-length sequence as a linear transform, it is easy to equivalently reform the input–output equation of linear discrete time-invariant and time-varying ILC systems as an algebraic discrete-frequency equation. Thus the derivative-type (D-type) iterative learning control (ILC) converges in a discrete-frequency domain if and only if it converges in a discrete-time domain. Numerical simulations are carried out to exhibit the validity and effectiveness.

State Feedback Synthesis for Discrete-time Linear Systems with Stochastic Parameters Guaranteeing Deterministic H2 Performance and Stochastic Stability

In this paper, we propose a design method of state feedback controllers for discrete-time linear systems whose state-space matrices contain stochastic parameters. For such systems, if the parameters fluctuate according to the normal distribution, it is impossible to strictly guarantee the “conventional deterministic control performance” due to the unlimited parameter variations. Then, in our problem setup, we consider incorporating the “stochastic stability” into the conventional deterministic H2 performance. We derive a design condition on state feedback controllers which achieve deterministic H2 performance and stochastic stability simultaneously in terms of linear matrix inequalities (LMIs) via extended LMI. The effectiveness of the proposed method is illustrated through a numerical example.

A Performance Analysis for Iterative Learning Control in the Presence of Observation Noise

Abstract This paper investigates tracking performances attainable in iterative learning control of linear discrete-time systems with unknown parameters in the presence of observation noise. The transient and steady-state performances are measured by the decay rate and the magnitude of tracking error, respectively. A trade-off relation between these performances is represented by the product of the direct terms of the plant and the learning law. Numerical simulations are conducted to observe the trade-off behaviors.

Iterative Learning Control for Discrete-time Linear Systems Through Fading Channels

In this paper, iterative learning control(ILC) is used to solve the problem of accurate tracking of random systems with fading channel. The fading problem is a type of multiplicative uncertainties, which is generally caused by unreliable communication networks. It is modeled by a random variable with prior statistics for correcting received signals. Both output fading case and input fading case are discussed in this paper. The P-type learning algorithms with a decreasing learning gain are proposed with almost sure convergence analysis. Illustrative simulations are provided to verify the theoretical results.

Semi-global containment control of discrete-time linear systems with actuator position and rate saturation

In this paper, we study semi-global containment control problem for a multi-agent system in the presence of multiple leader agents. We describe the dynamics of each follower agent in multi-agent system by a general discrete-time linear system subject to both actuator position and rate saturation. By using low gain approach, we construct both a linear state feedback control law and an observer-based output feedback control law for each follower agent. Under some standard assumptions, we provide a sufficient condition to guarantee that the states of follower agents converge to the convex hull formed by the leader agents asymptotically. Finally, we illustrate the theoretical results by numerical simulation results.

Estimation and stability over AWGN channel in the presence of fading, noisy feedback channel and different sample rates

This paper is concerned with estimation and stability of control systems over communication links subject to limited capacity, power constraint, fading, noisy feedback, and different transmission rate rather than system sampling rate. A key issue addressed in this paper is that in the presence of noisy feedback associated with channel, which models transmission of finite number of bits over such links as is the case in most practical scenarios, the well-known eigenvalues rate condition is still a tight bound for stability. Based on an information theoretic analysis, necessary conditions are derived for stability of discrete-time linear control systems via the distant controller in the mean square sense. By construction of a specific coding scheme and by the design of a proper controller, the tight sufficient conditions for stability of control systems are also derived for linear discrete-time control systems over both Additive White Gaussian Noise (AWGN) and fading channels. This implies that the proposed coding scheme is efficient. The results are presented with the mismatch assumption between channel symbol and plant sample rates. As one key result of this paper, it is shown that if the channel symbol rate is less than the system sample rate, the control system is still stabilizable via increasing the transmission power.

Iterative Learning Control for Linear Discrete-Time Systems with Randomly Variable Input Trail Length

For linear discrete-time systems with randomly variable input trail length, a proportional- (P-) type iterative learning control (ILC) law is proposed. To tackle the randomly variable input trail length, a modified control input at the desirable trail length is introduced in the proposed ILC law. Under the assumption that the initial state fluctuates around the desired initial state with zero mean, the designed ILC scheme can drive the ILC tracking errors to zero at the desirable trail length in expectation sense. The designed ILC algorithm allows the trail length of control input which is different from system state and output at a specific iteration. In addition, the identical initial condition widely used in conventional ILC design is also mitigated. An example manifests the validity of the proposed ILC algorithm.