We consider the stochastic optimal control problem of nonlinear mean-field systems in discrete time. We reformulate the problem into a deterministic control problem with marginal distribution as controlled state variable, and prove that dynamic programming principle holds in its general form. We apply our method for solving explicitly the mean-variance portfolio selection and the multivariate l...

We study a class of time-domain decomposition-based methods for the numerical solution of large-scale linear quadratic optimal control problems. Our methods are based on a multiple shooting reformulation of the linear quadratic optimal control problem as a discrete-time optimal control (DTOC) problem. The optimality conditions for this DTOC problem lead to a linear block tridiagonal system. The...

This paper studies the discrete-time sampled-data approximation of the input-constrained finite-horizon linear quadratic regulator problem. Explicit estimates for the error in the performance index rendered by the solution of a discrete-time approximation are provided. This result can be used to evaluate the level of sub-optimality of the sampled-data solution corresponding to a given discretis...

This paper presents the application of discrete-time variable structure control with sliding mode based on the ‘reaching law’ method for robust control of a ‘simple inverted pendulum on moving cart’ a standard nonlinear benchmark system. The controllers designed using the above techniques are completely insensitive to parametric uncertainty and external disturbance. The controller design is car...

In this paper we study the solution to optimal control problems for discrete time linear hybrid systems. First, we prove that the closed form of the state-feedback solution to finite time optimal control based on quadratic or linear norms performance criteria is a time-varying piecewise affine feedback control law. Then, we give an insight into the structure of the optimal state-feedback soluti...

The mathematical theory of optimal control consisting all the continuous and discrete systems is strong studied more than 40 years. L. S. Pontryagin et al. first obtained basic results of the theory of optimal control and then this theory was developed and simplificated by other academicians [1-4]. Gaishun presented a detailed works regarding the optimal control problem to multidimensional diff...

We consider constrained finite-time optimal control problems for discrete-time linear time-invariant systems with constraints on inputs and outputs based on linear and quadratic performance indices. The solution to such problems is a time-varying piecewise affine (PWA) state-feedback law and it can be computed by means of multiparametric programming. By exploiting the properties of the value fu...

We consider within the framework of the Mean Field Games theory a dynamic discrete choice model with social interactions, where a large number of agents/players are choosing between two alternatives while influenced by the group’s behavior. We introduce the “Min-LQG” optimal control problem, a modified Linear Quadratic Gaussian (LQG) optimal control problem that includes a minimum term in its f...

We consider symplectic difference systems, which contain as special cases linear Hamiltonian difference systems and Sturm–Liouville difference equations of any even order. An associated discrete quadratic functional is important in discrete variational analysis, and while its positive definiteness has been characterized and is well understood, a characterization of its positive semidefiniteness...