Control Of Discrete-time Linear Systems Research Articles

Periodic event-triggered state-feedback control for discrete-time linear systems

This paper investigates the periodic event-triggered control for discrete-time linear systems. The discrete-time plant denotes a combination of the continuous-time controlled plant, the sensors and the actuator. A general packaged component, event machine, is introduced to conduct the detection and judgement of the events. Then the periodic event-triggered control for the discrete-time system including a discrete-time plant, an event machine, a transmitter and a continuous static controller, exhibits some different behaviors from that for the continuous-time system. Especially, in this system, the sampling sequences and the event-verifying sequences may be independent from each other. Furthermore, according to the difference between the two sequences, the periodic event-triggered control system is classified into three cases, and the corresponding models are established for the three cases: a discrete-time perturbed linear system, a discrete time-delay system and a switched system, respectively. Moreover, the stability conditions for the three cases are proposed. Finally, a numerical example is given to illustrate the efficiency and feasibility of the obtained results.

Об оценивании состояний многошаговых систем при групповом движении

The reachability problem for linear discrete-time control systems which describe multi-agent motion is considered. Namely, we consider a finite set of subsystems with controls to be chosen under the condition that the trajectories of the subsystems are pairwise not very close to and not very far away from each other. Properties of reachable sets of such systems are described. Some algorithms for constructing external polyhedral (parallelepiped-valued) estimates for reachable sets are proposed.

Self-triggered control for communication reduction in networked systems

Abstract: We study networked control of linear discrete-time systems using self-triggered strategies to reduce the amount of communication. At each transmission, the controller determines the next transmission time in advance based on the current state. We propose three self-triggered strategies which guarantee control performance based on a quadratic cost function. They have different characteristics with respect to the computation load for finding the transmission times. Through a numerical example, we demonstrate the tradeoff between computation loads and transmission frequencies.

Structural Controllability of Discrete-Time Linear Control Systems with Time-Delay: A Delay Node Inserting Approach

This paper is concerned with the structural controllability analysis for discrete-time linear control systems with time-delay. By adding virtual delay nodes, the linear systems with time-delay are transformed into corresponding linear systems without time-delay, and the structural controllability of them is equivalent. That is to say, the time-delay does not affect or change the controllability of the systems. Several examples are also presented to illustrate the theoretical results.

Mean Square Stability Based on H∞ Control for Uncertain Networked Control Systems with Random Data Loss

This paper studies the design of uncertain linear discrete-time Networked Control Systems over imperfect communication channels with time-varying data loss. This leakage is modeled as stochastic parameter and norm-bounded uncertainties. In addition, this paper defines the necessary conditions for the design of the dynamic output feedback controller; subsequently, an iterative LMI approach is specified to compute the controller state parameters. The simulation results show that the designed controller improves the H∞ disturbance attenuation performance of the concerned uncertain system.

Computational Simulations on Stability of Model Predictive Control for Linear Discrete-time Stochastic Systems

Model predictive control is a kind of optimal feedback control in which control performance over a finite future is optimized with a performance index that has a moving initial time and a moving terminal time. This paper examines the stability of model predictive control for linear discrete-time systems with additive stochastic disturbances. A sufficient condition for the stability of the closed-loop system with model predictive control is derived by means of a linear matrix inequality. The objective of this paper is to show the results of computational simulations in order to verify the effectiveness of the obtained stability condition. Keywords—Computational simulations, optimal control, predictive control, stochastic systems, discrete-time systems.

A Spectral Characterization of Controllability for Linear Discrete-Time Systems with Conic Constraints

In this paper, we generalize all previously known results on the controllability of discrete-time linear systems with conic input and/or state constraints. In addition, we single out two cases of the problem which did not appear in the literature before. We provide a characterization for the first one of these new cases. For the second newly introduced case, we show that it is rare and pathological. Moreover, we show that the classical results cannot be extended to this last pathological case. These results altogether lead to an almost complete spectral characterization of controllability for discrete-time linear systems with conic input and/or state constraints.

State control of discrete-time linear systems to be bound in state variables by equality constraints

The paper is concerned with the problem of designing the discrete-time equivalent PI controller to control the discrete-time linear systems in such a way that the closed-loop state variables satisfy the prescribed equality constraints. Since the problem is generally singular, using standard form of the Lyapunov function and a symmetric positive definite slack matrix, the design conditions are proposed in the form of the enhanced Lyapunov inequality. The results, offering the conditions of the control existence and the optimal performance with respect to the prescribed equality constraints for square discrete-time linear systems, are illustrated with the numerical example to note effectiveness and applicability of the considered approach.

О свойстве равномерной полной управляемости линейной управляемой системы с дискретным временем

О свойстве равномерной полной управляемости линейной управляемой системы с дискретным временем

Stability analysis and failure tolerant control for discrete-time linear systems with controller failure

In this paper, the stability and failure tolerant control are investigated for discrete-time time-invariant linear systems with occasional controller failure due to physical or purposeful reason. By introducing the conceptions of minimal controller reliable time and maximal controller failure time, a novel time-varying piecewise quadratic Lyapunov function (TPQLF) approach is proposed to analyse the stability property of closed-loop system in presence of controller failure. The presented TPQLF method combines both merits of previous Lyapunov function based results such as common Lyapunov function and piecewise Lyapunov function approaches. Furthermore, based on TPQLF, the feasible region described by pairs of minimal controller reliable time and maximal controller failure time can be easily computed by an iterative algorithm. Then, on the basis of the analysis results, time-varying state feedback gains are formulated to construct failure tolerant controller. It is demonstrated that the time-varying structure of controller provides more failure tolerance capacity than time-invariant controller. Several numerical examples are given to illustrate our theoretic findings in this paper.

New forms of Riccati equations and the further results of the optimal control for linear discrete-time systems

For linear discrete-time systems, the traditional finite horizon optimal controller is proved to render the closed-loop systems asymptotically stable under some assumptions in literature. In this paper, a new form of finite horizon discrete-time Riccati equation is proposed. It is proved that the new form of finite horizon discrete-time Riccati equation is equivalent to the other three old ones. Based on this new form of finite horizon discrete-time Riccati equation, the finite horizon optimal controller of linear discrete time systems is proved to render the closed-loop system exponentially stable without any assumptions. At the same time, a new form of infinite horizon discrete-time Riccati equation is proposed when the discrete system is controllable or stabilizable. It is proved that the new form of infinite horizon discrete-time Riccati equation is equivalent to the other three old ones too. Based on this new form of infinite horizon discrete-time Riccati equation, the infinite horizon optimal controller of linear discrete-time systems is proved to render the closed-loop system exponentially stable when the open-loop system is either controllable or stabilizable. Finally an unstable batch reactor and an unstable inverted pendulum are used to verify the theory results of this paper.

Согласованность дискретных линейных стационарных управляемых систем с неполной обратной связью специального вида для n=5

Согласованность дискретных линейных стационарных управляемых систем с неполной обратной связью специального вида для n=5

Quadratic and H∞ switching control for discrete-time linear systems with multiplicative noises

The goal of this paper is to study the switched stochastic control problem of discrete-time linear systems with multiplicative noises. We consider both the quadratic and the H∞ criteria for the performance evaluation. Initially we present a sufficient condition based on some Lyapunov–Metzler inequalities to guarantee the stochastic stability of the switching system. Moreover, we derive a sufficient condition for obtaining a Metzler matrix that will satisfy the Lyapunov–Metzler inequalities by directly solving a set of linear matrix inequalities, and not bilinear matrix inequalities as usual in the literature of switched systems. We believe that this result is an interesting contribution on its own. In the sequel we present sufficient conditions, again based on Lyapunov–Metzler inequalities, to obtain the state feedback gains and the switching rule so that the closed loop system is stochastically stable and the quadratic and H∞ performance costs are bounded above by a constant value. These results are illustrated with some numerical examples.

New Results on Output Feedback <formula formulatype="inline"> <tex Notation="TeX">$H_{\infty} $</tex></formula> Control for Linear Discrete-Time Systems

This note investigates the problem of output feedback H∞ control for linear discrete-time systems. Three types of H∞ controllers are considered, namely, static output feedback controllers, dynamic output feedback controllers, and observer-based output feedback controllers. New design conditions for the three type of output feedback controllers are introduced in terms of unified linear matrix inequality (LMI) representations, which guarantee the prescribed H∞ performances of the closed-loop systems. In contrast to the existing LMI conditions for designing the output feedback H∞ controllers, the improvement of the proposed results over the existing ones is shown by theoretical proof and numerical example.

U-D factorisation of the strengthened discrete-time optimal projection equations

Algorithms for optimal reduced-order dynamic output feedback control of linear discrete-time systems with white stochastic parameters are U-D factored in this paper. U-D factorisation enhances computational accuracy, stability and possibly efficiency. Since U-D factorisation of algorithms for optimal full-order output feedback controller design was recently published by us, this paper focusses on the U-D factorisation of the optimal oblique projection matrix that becomes part of the solution as a result of order-reduction. The equations producing the solution are known as the optimal projection equations which for discrete-time systems have been strengthened in the past. The U-D factored strengthened discrete-time optimal projection equations are presented in this paper by means of a transformation that has to be applied recursively until convergence. The U-D factored and conventional algorithms are compared through a series of examples.

Observer-based output feedback control of discrete-time linear systems with input and output delays

In this paper, we study observer-based output feedback control of discrete-time linear systems with both multiple input and output delays. By generalising our recently developed truncated predictor feedback approach for state feedback stabilisation of discrete-time time-delay systems to the design of observer-based output feedback, two types of observer-based output feedback controllers, one being memory and the other memoryless, are constructed. Both full-order and reduced-order observer-based controllers are established in both the memory and memoryless schemes. It is shown that the separation principle holds for the memory observer-based output feedback controllers, but does not hold for the memoryless ones. We further show that the proposed observer-based output feedback controllers solve both the l2 and l∞ semi-global stabilisation problems. A numerical example is given to illustrate the effectiveness of the proposed approaches.

К свойству согласованности четырехмерных дискретных линейных стационарных управляемых систем с неполной обратной связью специального вида

К свойству согласованности четырехмерных дискретных линейных стационарных управляемых систем с неполной обратной связью специального вида

Reinforcement [formula omitted]-learning for optimal tracking control of linear discrete-time systems with unknown dynamics

In this paper, a novel approach based on the Q-learning algorithm is proposed to solve the infinite-horizon linear quadratic tracker (LQT) for unknown discrete-time systems in a causal manner. It is assumed that the reference trajectory is generated by a linear command generator system. An augmented system composed of the original system and the command generator is constructed and it is shown that the value function for the LQT is quadratic in terms of the state of the augmented system. Using the quadratic structure of the value function, a Bellman equation and an augmented algebraic Riccati equation (ARE) for solving the LQT are derived. In contrast to the standard solution of the LQT, which requires the solution of an ARE and a noncausal difference equation simultaneously, in the proposed method the optimal control input is obtained by only solving an augmented ARE. A Q-learning algorithm is developed to solve online the augmented ARE without any knowledge about the system dynamics or the command generator. Convergence to the optimal solution is shown. A simulation example is used to verify the effectiveness of the proposed control scheme.

On Extended LMI Conditions for ℋ2/ℋ∞ Control of Discrete-Time Linear Systems

This paper provides new insights into the currently available extended linear matrix inequality (LMI) conditions for control of discrete-time linear systems, motivating the use of two intrinsically different extended LMI characterizations for ℋ2 performance. While these conditions are equivalent for ℋ2 analysis and many ℋ2 control problems related to precisely known linear time-invariant (LTI) systems, they generally yield different results when employed for multi-objective ℋ2/ℋ∞ control and ℋ2 analysis and control of uncertain linear systems. The advantage of considering both the ℋ2 LMIs for robust ℋ2 state feedback and multi-objective ℋ2/ℋ∞ control design is demonstrated by means of exhaustive numerical comparisons.

Multiparameter Fractional Difference Linear Control Systems

The Riemann-Liouville-, Caputo-, and Grünwald-Letnikov-type fractional order difference operators are discussed and used to state and solve the controllability and observability problems of linear fractional order discrete-time control systems with multiorder and multistep. It is shown that the obtained results do not depend on the type of fractional operators and steps. The comparison of systems is made under the number of steps needed, firstly to achieve a final point, and secondly to distinguish initial conditions for particular operator.