2006· Journal of Convex Analysis· 0 citations· 27 references
Abstract
We investigate here a continuous time minimization problem in the presence of disturbances in the dynamics. The only information available to the controller is an incomplete observation of the state space at times given in advance. Also, the initial state is not supposed to be perfectly known. The corresponding control problem can be understood as a dynamic game of Min-Max type where the controller wants to minimize the cost – by choosing a strategy depending on a discrete-time incomplete measurement – against the worst case of disturbance and initial state. Our main goal is to pass from imperfect information in the measurement space to perfect information in the estimation space, hence we introduce a second problem based on estimation sets on the state. We prove that the value functions of both problems are equal. Finally, we provide a characterization of the value function through a system of Hamilton-Jacobi equations and inequalities in terms of Dini derivatives.
We consider systems that are governed by linear time-discrete dynamics with an initial condition and a terminal condition for the expected values. We study optimal control problems where in the objective function a term of tracking type for the expected values and a control cost appear. In addition, the feasible states...
M. Gugat, H. Heitsch, R. Henrion· Journal of Convex Analysis· 2 citations
This paper aims to describe a synthesis procedure for discrete-time, energy-based regulators for continuous-time port-Hamiltonian systems. The methodology consists of three steps. The first deals with the definition of a discrete-time approximation of the plant, which is subsequently employed in the development of the...
This article investigates the problem of data-driven control design for unknown linear discrete-time systems with time-varying delays, where the controller gains are learned from input-state data affected by multiple perturbations. First, considering that the available measurements may be affected by noise, errors, and...
Yu Fan, Chuan-Ke Zhang, Jing Song et al.· IEEE Transactions on Cyberne...· 0 citations
This paper considers the reach-stabilize prob- lem for a class of nonlinear control-affine systems with unknown parametric uncertainties, where the system states must remain in a safe set at all times, or enter a safe set in finite time and then remain in it, and converge to a goal point. An estimator is designed that...
In this paper, we consider the control of Markov jump linear systems when the active system mode is not exactly known. We rather assume that this true mode is only known to belong to an observed cluster of modes, making both the dynamics and the associated transition probabilities uncertain. We construct a min-max opti...
C. Persiani, Ram Padmanabhan, M. Ornik et al.· 0 citations
