scholarly journals A computational method for a class of jump linear quadratic systems

1995 ◽  
Vol 36 (4) ◽  
pp. 414-423
Author(s):  
K. H. Wong ◽  
N. Lock ◽  
K. Kaji
Keyword(s):  
Nonlinear Programming ◽  
Feedback Control ◽  
Stochastic Control ◽  
Optimization Problem ◽  
Original Problem ◽  
Computational Method ◽  
Control Law ◽  
Linear Quadratic ◽  
Programming Technique ◽  
Parameter Values

AbstractA class of linear systems subject to sudden jumps in parameter values is considered. To solve this class of stochastic control problem, we try to seek the best feedback control law depending only on the measurable output. Based on this idea, we convert the original problem into an approximate constrained deterministic optimization problem, which can be easily solved by any existing nonlinear programming technique. An example is solved to illustrate the efficiency of the method.

Bifurcation Control of Ro¨ssler System

2003 ◽  
Author(s):  
Z. Q. Wu ◽  
P. Yu
Keyword(s):  
Feedback Control ◽  
Nonlinear Dynamical Systems ◽  
Equilibrium Points ◽  
New Method ◽  
Control Law ◽  
Equilibrium Solutions ◽  
Nonlinear Dynamical ◽  
The Stability ◽  
Parameter Values ◽  
Feasible System

In this paper, a new method is proposed for controlling bifurcations of nonlinear dynamical systems. This approach employs the idea used in deriving the transition variety sets of bifurcations with constraints to find the stability region of equilibrium points in parameter space. With this method, one can design, via a feedback control, appropriate parameter values to delay either static, or dynamic or both bifurcations as one wishes. The approach is applied to consider controlling bifurcations of the Ro¨ssler system. The uncontrolled Ro¨ssler has two equilibrium solutions, one of which exhibits static bifurcation while the other has Hopf bifurcation. When a feedback control based on the new method is applied, one can delay the bifurcations and even change the type of bifurcations. An optimal control law is obtained to stabilize the Ro¨ssler system using all feasible system parameter values. Numerical simulations are used to verify the analytical results.

Suboptimality of a Decentralized Feedback Control Law

1999 ◽  
Vol 121 (2) ◽  
pp. 305-308
Author(s):  
El Kebi´r Boukas ◽  
A. Swierniak ◽  
H. Yang
Keyword(s):  
Feedback Control ◽  
Linear System ◽  
Upper Bound ◽  
Optimization Problem ◽  
Control Law ◽  
Relative Cost ◽  
Numerical Example ◽  
Uncertain Linear System ◽  
The Absolute ◽  
The Cost

In this note, a new estimating method for the upper bound of the cost of the uncertain linear system used by Trinh and Aldeen (1993) is proposed. We have also estimated the absolute cost loss and relative cost loss of this kind of optimization problem. To show the usefulness of our results a numerical example has been developed.

scholarly journals Linear Quadratic Optimal Control Design: A Novel Approach Based on Krotov Conditions

2019 ◽  
Vol 2019 ◽  
pp. 1-17
Author(s):  
Avinash Kumar ◽  
Tushar Jain
Keyword(s):  
Optimal Control ◽  
Cost Function ◽  
Riccati Equation ◽  
Nonconvex Optimization ◽  
Optimization Problem ◽  
A Priori ◽  
Control Law ◽  
Linear Quadratic ◽  
Linear Quadratic Optimal Control ◽  
Quadratic Optimal Control

This paper revisits the problem of synthesizing the optimal control law for linear systems with a quadratic cost. For this problem, traditionally, the state feedback gain matrix of the optimal controller is computed by solving the Riccati equation, which is primarily obtained using calculus of variations- (CoV-) based and Hamilton–Jacobi–Bellman (HJB) equation-based approaches. To obtain the Riccati equation, these approaches require some assumptions in the solution procedure; that is, the former approach requires the notion of costates and then their relationship with states is exploited to obtain the closed-form expression of the optimal control law, while the latter requires a priori knowledge regarding the optimal cost function. In this paper, we propose a novel method for computing linear quadratic optimal control laws by using the global optimal control framework introduced by V. F. Krotov. As shall be illustrated in this article, this framework does not require the notion of costates and any a priori information regarding the optimal cost function. Nevertheless, using this framework, the optimal control problem gets translated to a nonconvex optimization problem. The novelty of the proposed method lies in transforming this nonconvex optimization problem into a convex problem. The convexity imposition results in a linear matrix inequality (LMI), whose analysis is reported in this work. Furthermore, this LMI reduces to the Riccati equation upon imposing optimality requirements. The insights along with the future directions of the work are presented and gathered at appropriate locations in this article. Finally, numerical results are provided to demonstrate the proposed methodology.

A Genetic Algorithm for Solving Linear-Quadratic Bilevel Program-Ming Problems

2011 ◽  
Vol 186 ◽  
pp. 626-630
Author(s):  
He Cheng Li ◽  
Yu Ping Wang
Keyword(s):  
Genetic Algorithm ◽  
Nonlinear Programming ◽  
Programming Problem ◽  
Original Problem ◽  
Nonlinear Programming Problem ◽  
Linear Quadratic ◽  
Bilevel Programming Problem ◽  
Equivalent Problem ◽  
Bilevel Program ◽  
Two Phases

In this paper, we focus on a special linear-quadratic bilevel programming problem in which the follower’s problem is a convex-quadratic programming, whereas the leader’s functions are linear. At first, based on Karush-Kuhn-Tucher(K-K-T) conditions, the original problem is transformed into an equivalent nonlinear programming problem in which the objective and constraint functions are linear except for the complementary slack conditions. Then, a genetic algorithm is proposed to solve the equivalent problem. In the proposed algorithm, the individuals are encoded in two phases. Finally, the efficiency of the approach is demonstrated by an example.

Universal Feedback Controllers and Inverse Optimality for Nonlinear Stochastic Systems

2019 ◽  
Vol 142 (2) ◽  
Author(s):  
Wassim M. Haddad ◽  
Xu Jin
Keyword(s):  
Dynamical Systems ◽  
Feedback Control ◽  
Stochastic Control ◽  
Stochastic Systems ◽  
Sufficient Conditions ◽  
Optimal Feedback Control ◽  
Control Law ◽  
Stochastic Dynamical Systems ◽  
Control Lyapunov Function ◽  
Inverse Optimality

Abstract In this paper, we develop a constructive finite time stabilizing feedback control law for stochastic dynamical systems driven by Wiener processes based on the existence of a stochastic control Lyapunov function. In addition, we present necessary and sufficient conditions for continuity of such controllers. Moreover, using stochastic control Lyapunov functions, we construct a universal inverse optimal feedback control law for nonlinear stochastic dynamical systems that possess guaranteed gain and sector margins. An illustrative numerical example involving the control of thermoacoustic instabilities in combustion processes is presented to demonstrate the efficacy of the proposed framework.

scholarly journals Optimal Stochastic Control in the Interception Problem of a Randomly Tacking Vehicle

Mathematics ◽  
2021 ◽  
Vol 9 (19) ◽  
pp. 2386
Author(s):  
Andrey A. Galyaev ◽  
Pavel V. Lysenko ◽  
Evgeny Y. Rubinovich
Keyword(s):  
Stochastic Control ◽  
Optimization Problem ◽  
Optimal Solution ◽  
Threshold Value ◽  
Optimal Stochastic Control ◽  
Control Law ◽  
Stochastic Problem ◽  
Deterministic Problem ◽  
Analytical Estimation ◽  
Suboptimal Solution

This article considers the mathematical aspects of the problem of the optimal interception of a mobile search vehicle moving along random tacks on a given route and searching for a target, which travels parallel to this route. Interception begins when the probability of the target being detected by the search vehicle exceeds a certain threshold value. Interception was carried out by a controlled vehicle (defender) protecting the target. An analytical estimation of this detection probability is proposed. The interception problem was formulated as an optimal stochastic control problem, which was transformed to a deterministic optimization problem. As a result, the optimal control law of the defender was found, and the optimal interception time was estimated. The deterministic problem is a simplified version of the problem whose optimal solution provides a suboptimal solution to the stochastic problem. The obtained control law was compared with classic guidance methods. All the results were obtained analytically and validated with a computer simulation.

Guaranteed Asymptotic Output Stability for Systems With Constant Disturbances

1987 ◽  
Vol 109 (2) ◽  
pp. 186-189 ◽  
Author(s):  
W. E. Schmitendorf ◽  
B. R. Barmish
Keyword(s):  
Feedback Control ◽  
Linear Systems ◽  
State Feedback ◽  
Initial Conditions ◽  
State Feedback Control ◽  
Control Law ◽  
Uncertain Parameters ◽  
Output Stability ◽  
Linear State ◽  
Parameter Values

For a class of linear systems in which there are uncertain parameters in the system and input matrices, as well as constant additive disturbances, a linear state feedback control law is derived. The only information available about the uncertain parameters is the bounding sets in which they lie. The design guarantees that the specified output approaches zero for all possible parameter values and for all initial conditions. Two examples illustrate the application of the theory.

Optimization approach to the constrained regulation problem for linear continuous-time fractional-order systems

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Xindong Si ◽  
Hongli Yang
Keyword(s):  
Feedback Control ◽  
Fractional Order ◽  
State Feedback Control ◽  
Invariant Sets ◽  
Linear Feedback ◽  
Control Law ◽  
Optimization Approach ◽  
Fractional Order Systems ◽  
Linear Feedback Control ◽  
Computational Point

AbstractThis paper deals with the Constrained Regulation Problem (CRP) for linear continuous-times fractional-order systems. The aim is to find the existence conditions of linear feedback control law for CRP of fractional-order systems and to provide numerical solving method by means of positively invariant sets. Under two different types of the initial state constraints, the algebraic condition guaranteeing the existence of linear feedback control law for CRP is obtained. Necessary and sufficient conditions for the polyhedral set to be a positive invariant set of linear fractional-order systems are presented, an optimization model and corresponding algorithm for solving linear state feedback control law are proposed based on the positive invariance of polyhedral sets. The proposed model and algorithm transform the fractional-order CRP problem into a linear programming problem which can readily solved from the computational point of view. Numerical examples illustrate the proposed results and show the effectiveness of our approach.

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