Stochastic optimal linear feedback control systems using available measurements

A general result in stochastic optimal control of nonlinear discrete-time systems with quadratic performance criteria

In this article, we prove the continuity property of the Combined $L^{1}-L^{2}$ (CLOT) optimal control for linear systems. For this, we give first-order necessary conditions for the CLOT optimal control problem based on the non-smooth maximum principle. From these necessary conditions, we prove that if the problem is normal, then the CLOT optimal control (if it exists) is continuous with respect to time. Simulation results are shown to illustrates the continuity property of the CLOT optimal control.

The optimal control of linear systems where measurement of all the state variables is not possible is investigated from the viewpoint of observer theory. Observers whose dynamic order equals the dimension of the plant state vector are examined and necessary conditions for the optimal observer dynamics and control feedback gains are derived.

Optimal linear regulator problems solved by the finite element method

On stochastic dynamic stackelberg strategies

On Stochastic Dynamic Stackelberg Strategies

We consider a finite-horizon linear-quadratic optimal control problem where only a limited number of control messages are allowed for sending from the controller to the actuator. To restrict the number of control actions computed and transmitted by the controller, we employ a threshold-based event-triggering mechanism that decides whether or not a control message needs to be calculated and delivered. Due to the nature of threshold-based event-triggering algorithms, finding the optimal control sequence requires minimizing a quadratic cost function over a nonconvex domain. In this paper, we first provide an exact solution to this nonconvex problem by solving an exponential number of quadratic programs. To reduce computational complexity, we then propose two efficient heuristic algorithms based on greedy search and the alternating direction method of multipliers technique. Later, we consider a receding horizon control strategy for linear systems controlled by event-triggered controllers, and we further provide a complete stability analysis of receding horizon control that uses finite-horizon optimization in the proposed class. Numerical examples testify to the viability of the presented design technique.

Stochastic optimal control of unknown linear networked control system in the presence of random delays and packet losses

This correspondence considers the problem of optimal regulator design for discrete time linear systems subjected to white state-dependent and control-dependent noise in addition to additive white noise in the input and the observations. A pseudo-deterministic problem is first defined in which multiplicative and additive input disturbances are present, but noise-free measurements of the complete state vector are available. This problem is solved via discrete dynamic programing. Next is formulated the problem in which the number of measurements is less than that of the state variables and the measurements are contaminated with state-dependent noise. The inseparability of control and estimation is brought into focus, and an enforced separation solution is obtained via heuristic reasoning in which the control gains are shown to be the same as those in the pseudo-deterministic problem. An optimal linear state estimator is given in order to implement the controller.

The satisfactory optimal control of linear systems under the existence of disturbance is studied. The satisfactory optimal control optimizes a quadratic maximal-valued objective functional subject to the H/sub /spl infin// norm constraint. We obtain Riccati-type equations by which the satisfactory optimal control is calculated in a form of state feedback.

Optimal control for linear systems described by $m$-times integrated semigroups

Time optimal control for linear systems on Lie groups

Fuzzy Optimal Control of Linear Systems. Part 1. Positional Control

Optimal feedback stabilization policy with asymmetric loss functions

Algorithms are currently available for the solution of certain types of optimal-eigenvalue-assignment problems in which the eigenvalues of a given system are required to be shifted into preassigned locations or region while also minimising an appropriate quadratic-performance criterion. All the known methods for a solution of the above problem are based on manipulation of the original nth-order system matrices even if only r eigenvalues (r ≥ n) of the original system are to be reassigned. On the contrary, the method proposed in this paper, for a solution of the above problem, employs an rth-order equivalent model, which leads to a solution via manipulation of rth-order matrices only. The method also ensures that the remaining n — r eigenvalues of the original system are not disturbed and are carried over to the resultant feedback system. It has been shown in the paper that the suggested procedure brings about a considerable saving in computation time, and also requires less computer storage. Two numerical examples have been included to illustrate the suggested technique.