Time-delays are important components of many dynamical systems that describe coupling or interconnection between dynamics, propagation or transport phenomena, and heredity and competition in population dynamics. The stabilization with time delay in observation or control represents difficult mathematical challenges in the control of distributed parameter systems. It is well-known that the stabi...

This paper studies the exponential stabilization problem for discrete-time switched linear systems based on a control-Lyapunov function approach. It is proved that a switched linear system is exponentially stabilizable if and only if there exists a piecewise quadratic control-Lyapunov function. Such a converse control-Lyapunov function theorem justifies many of the earlier synthesis methods tha...

In this paper, the linear-quadratic optimal control problem is considered for discretetime stochastic systems with indefinite weight matrices in the cost function and mean-field terms in both the cost function and system dynamics. A set of generalized difference Riccati equations (GDREs) is introduced in terms of algebraic equality constraints and matrix pseudo-inverse. It is shown that the sol...

We investigate turnpike behaviour of discrete time optimal control problems with linear dynamics and linear-quadratic cost functions including state and control constraints. We give necessary and sufficient conditions in terms of spectral criteria and matrix inequalities. As important tools we use the concepts of strict dissipativity and a new property called strict pre-dissipativity of a syste...

Inspired by the successes of stochastic algorithms in training deep neural networks and simulation interacting particle systems, we propose analyze a framework for randomized time-splitting linear-quadratic optimal control. In our proposed framework, linear dynamics original problem is replaced dynamics. To obtain dynamics, system matrix split into simpler submatrices time interval interest sub...

Discrete-time coupled algebraic Riccati equations that arise in quadratic optimal control and -control of Markovian jump linear systems are considered. First, the L_ equations that arise from the quadratic optimal control problem are studied. The matrix cost is only assumed to be hermitian. Conditions for existence of the maximal hermitian solution are derived in terms of the concept of mean sq...

The study of linear control problems with exponential-ofquadratic cost function was initiated in Jacobson (1973) where the author studies discrete-time and continuoustime state feedback problems. The discrete-time linear output feedback problems with exponential-of-quadratic cost function is studied in Whittle (1981). Bensousssan and Schuppen (1985) studied the continuous-time output feedback p...

This paper studies a linear-quadratic control problem for discretetime switched systems with subsystems perturbed by uncertainty. Analytical expressions are derived for both the optimal objective function and the optimal switching strategy. A two-step pruning scheme is developed to efficiently solve such problem. The performance of this method is shown by two examples.

New dual problems emphasizing decomposability are established for a general class of stochastic dynamic optimization problems, with piecewise linearquadratic objective function. Optimality conditions are derived which emphasize decomposition. The dual dynamics are conditioned on the available system state information, and this leads to a symmetry that is well-suited to computational methods suc...