Optimal Output Feedback Control Problem Research Articles

Control for networked control systems with multiplicative noises, packet dropouts and multiple delays

This paper mainly focuses on the optimal output feedback control problem for networked control systems (NCSs) involving multiplicative noises, packet dropouts, input delays and measurement delays. The main contributions of this paper can be concluded as follows. Firstly, different from the previous results, this paper overcomes the barrier of the packet dropouts and measurement delays. Based on the measurement data, the optimal estimator is given. Secondly, by using maximum principle, a sufficient and necessary condition for the optimal control problem is presented. Moreover, the explicit output feedback controller is derived with feedback gain based on the coupled Riccati difference equations. Numerical example is illustrated to show the effectiveness of the proposed algorithm.

Optimal Control for Networked Control Systems with Markovian Packet Losses

This paper is concerned with the optimal output feedback control problem for networked control systems (NCSs) with Markovian packet losses. In this paper, the packet losses occur both between the sensor and controller and between the controller and actuator. Moreover, the packet loss channels are described with two-state Markov chains. Since the precise state information cannot be obtained, thus an optimal recursive estimator is designed. Furthermore, by adopting the dynamic programming approach, we derive the optimal output feedback control, which is based on the solution to a given modified Riccati equation. The obtained results can be seen as an important implementation of the control theory for NCSs with unreliable communication channels.

Optimal output feedback control for discrete‐time Markov jump linear system with input delay and packet losses

SummaryThis article investigates the optimal output feedback control problem for discrete‐time Markov jump linear system (MJLS) with input delay and packet losses in finite horizon. There are three main contributions. First, we assume that the state variable and the jump variable are available to the controller, and then we propose a new version of stochastic maximum principle. Based on the new proposed tool, an optimal state feedback controller is obtained by solving a set of delayed coupled difference Riccati equations. Second, under the condition that the state variable is unavailable to the controller, it is desired to design a dynamic Markovian jump controller such that the closed‐loop system minimizes the performance index. Thus, an optimal Markovian jump linear filter is proposed for MJLS with input delay and packet losses. Finally, based on the optimal filter, we prove that the separation principle holds for this case and then an optimal output feedback controller is presented. Some numerical examples are presented to illustrate the proposed approach.

Adaptive fuzzy output feedback inverse optimal control for vehicle active suspension systems

In this paper, the adaptive fuzzy inverse optimal output feedback control problem for vehicular active suspension systems (ASSs) is addressed. The considered vehicular active suspension system (ASS) is a quarter-car model with electromagnetic actuators and contains unknown nonlinear characteristics. The fuzzy logic systems (FLSs) are used to approximate unknown nonlinearities, and an auxiliary system model is constructed. Based on auxiliary system model, a fuzzy state observer is designed to estimate immeasurable states. By using adaptive backstepping design technique and inverse optimal principle, an adaptive fuzzy output feedback inverse optimal strategy is proposed. The developed adaptive fuzzy inverse optimal output feedback control method not only guarantees that the attitude of the vehicle is stabilized, but also achieves inverse optimization in relation to the cost functional. Finally, the simulation studies are given in the cases of both bump road and sinusoid road displacement input, and the simulation results show the validity of the proposed control method.

Observer-Based Fuzzy Adaptive Inverse Optimal Output Feedback Control for Uncertain Nonlinear Systems

In this article, an observer-based fuzzy adaptive inverse optimal output feedback control problem is studied for a class of nonlinear systems in strict-feedback form. The considered nonlinear systems contain unknown nonlinear dynamics and their states are not measured directly. Fuzzy logic systems are applied to identify the unknown nonlinear dynamics and an auxiliary nonlinear system is constructed. Based on this auxiliary system, a fuzzy state observer is first designed to estimate the immeasurable states. By using the inverse optimal principle and adaptive backstepping design theory, an observer-based fuzzy adaptive inverse optimal output feedback control scheme is then developed. The proposed inverse optimal control scheme need not assume that the states are measurable. It also guarantees that the closed-loop system is semiglobally uniformly ultimately bounded, and achieves the optimal control objective as well. Finally, two simulation examples are provided to check the validity of the presented control method.

Further results on stabilization for NCSs with packet losses and transmission delay: UDP case

The stabilization problem concerning the user datagram protocol (UDP) for networked control systems (NCSs) is investigated in this paper. More specifically, both the state and control signal can be lost during transmission, and the networked induced delay occurs while the control signal delivered to the actuator. On the other hand, no communication channel can be accessed from the actuator to the estimator (no acknowledge signal). The innovations of this paper include: (1) Based on the modified Riccati-ZXL equations, the necessary and sufficient stabilization conditions are developed for the NCSs with packet losses and transmission delay (UDP case); (2) We have verified that the separation principle holds for the finite horizon optimal output feedback control problem; (3) For 1-dimensional case, the maximal delay bound and the maximal packet losses rate are derived.

Decentralized control scheme for large-scale systems defined over a graph in presence of communication delays and random missing measurements

This paper studies the decentralized output-feedback control of large-scale systems defined over a directed connected graph with communication delay and random missing measurements. The nodes in the graph represent the subsystems, and the edges represent the communication connection. The information travels across an edge in the graph and suffers from one step communication delay. For saving the storage space, the information delayed more than D step times is discarded. In addition, to model the system in a more practical case, we assume that the observation for the subsystem output suffers random missing. Under this new information pattern, the optimal output-feedback control problem is non-convex, what is worse, the separation principle fails. This implies that the optimal control problem with the information pattern introduced above is difficult to solve. In this paper, a new decentralized control scheme is proposed. In particular, a new estimator structure and a new controller structure are constructed, and the gains of the estimator and the controller are designed simultaneously. An optimality condition with respect to the gains is established. Based on the optimality condition, an iterative algorithm is exploited to design the gains numerically. It is shown that the exploited algorithm converges to Nash optimum. Finally, the proposed theoretical results are illustrated by a physical system which is a heavy duty vehicles platoon.

Output-Feedback Control of Unknown Linear Discrete-Time Systems With Stochastic Measurement and Process Noise via Approximate Dynamic Programming.

This paper studies the optimal output-feedback control problem for unknown linear discrete-time systems with stochastic measurement and process noise. A dithered Bellman equation with the innovation covariance matrix is constructed via the expectation operator given in the form of a finite summation. On this basis, an output-feedback-based approximate dynamic programming method is developed, where the terms depending on the innovation covariance matrix are available with the aid of the innovation covariance matrix identified beforehand. Therefore, by iterating the Bellman equation, the resulting value function can converge to the optimal one in the presence of the aforementioned noise, and the nearly optimal control laws are delivered. To show the effectiveness and the advantages of the proposed approach, a simulation example and a velocity control experiment on a dc machine are employed.

M-measurements Indefinite Linear Quadratic Optimal Control for Bilinear Stochastic Systems with Multiplicative Noises

The finite horizon indefinite linear quadratic (LQ) optimal output feedback control problem for discrete time stochastic systems with multiplicative noises and disturbed measurements is considered. In this problem, the weighting matrices of the quadratic cost functional are indefinite, and the optimal control does have the so-called dual effect. In order to make a compromise between the optimality and the computation complexity, a kind of M-measurements feedback control design approach is adopted. Based on the dynamic programming, the M-measurements feedback control for the bilinear stochastic systems (BLSS), which incorporates future measurements into the current control computation, can be solved in backward time, and the optimal solution is given in terms of a kind of generalized difference Riccati equation of the same dimensions as that of the plant. Simulation results show the superiority of the proposed algorithm over other widely used methods based on the certainty equivalence.

A CSCAD Software for Optimal Output Feedback Regulators

The optimal output feedback control problem concerns the problem of generating the control variables directly by using linear combination of the available output variables.This paper present a CSCAD software in detail.With this CSCAD software, the designer of control systems can obtain an optimal output feedback regulators subject t twelve kinds of performance indices(six kinds of indices for continuous system, six kinds of indices for discrete system).First, the gradient formulae for the indices sind an algorithm- based on gradient minimization technique are given.Then, the program flow-chart and examples are given.

Minimal root sensitivity in linear systems

Nominal performance, root (eigenvalue) sensitivity, and stability are important control design considerations. This paper deals only with the first two of these concerns. A lower bound is derived for root sensitivity and necessary and sufficient conditions are given for achieving this minimum. This is the main result of the paper. In addition, an optimal output feedback control problem is discussed which penalizes an index related to root sensitivity. Two hazards are clarified concerning root sensitivity designs. First, we illustrate that root sensitivity has nothing to do with stability. Secondly, we show that normality of the plant matrix is the necessary and sufficient condition for minimal root sensitivity, but that normality measures can be convex even when root sensitivity measures are not. Hence, the optimization problems are quite different.

Minimal Root Sensitivity in Linear Systems

Nominal performance, root (eigenvalue) sensitivity, and stability are important control design considerations. This paper deals only with the first two of these concerns. A lower bound is derived for root sensitivity and necessary and sufficient conditions are given for achieving this minimum. This is the main result of the paper. In addition, an optimal output feedback control problem is discussed which penalizes an index related to root sensitivity. Two hazards are clarified concerning root sensitivity designs. First, we illustrate that root sensitivity has nothing to do with stability. Secondly, we show that normality o the plant matrix is the necessary and sufficient condition for minimal root sensitivity, but that normality measures can be convex even when root sensitivity measures are not. Hence, theoptimization problems are quite different.