Abstract. In this paper, we formulate a general time-inconsistent stochastic linear–quadratic (LQ) control problem. The time-inconsistency arises from the presence of a quadratic term of the expected state as well as a state-dependent term in the objective functional. We define an equilibrium, instead of optimal, solution within the class of open-loop controls, and derive a sufficient condition...

In this paper we present stability and convergence results for Dynamic Programming-based reinforcement learning applied to Linear Quadratic Regulation (LQR). The spe-ciic algorithm we analyze is based on Q-learning and it is proven to converge to the optimal controller provided that the underlying system is controllable and a particular signal vector is persistently excited. The performance of ...

The adaptive linear quadratic Gaussian control problem, where the linear transformation of the state A and the linear transformation of the control B are unknown, is solved assuming only that (A; B) is controllable and (A; Q 1 ) is observable, where Q 1 determines the quadratic form for the state in the integrand of the cost functional. A weighted least squares algorithm is modified by using a ...

We apply the recently developed duality methods based on information relaxations to the classic linear quadratic (LQ) control problem. We derive two dual optimal penalties for the LQ problem when the control space is unconstrained. These two penalties, which are derived using value function and gradient methods, respectively, may be used to evaluate sub-optimal policies for constrained LQ probl...

We discuss the numerical solution of linear quadratic optimal control problems for descriptor systems. The classical solution approach for these problems requires the computation of deeating subspaces of structured pencils. We extend the recently developed methods 6] for Hamiltonian matrices to the general case of embedded pencils as they arise in descriptor systems.

This paper studies a new approach to linear quadratic control for linear systems with input saturation. Our work presents an optimal sector bound to model the mismatch between the unsaturated controller and saturated one and an optimised control design associated with this sector bound. This leads to a new characterisation of invariant sets and new switching controllers. The main outcome of thi...

In this paper we discuss the standard LQG control problem for linear, finite-dimensional time-invariant systems without any assumptions on the system parameters. We give an explicit formula for the infimum over all internally stabilizing strictly proper compensators and give a characterization when the infimum is attained.

A, B, C = state-space matrices a = acceleration due to linear-quadratic-regulatorand artificial-potential-field-determined control effort aAPF = acceleration due to artificial-potential-fielddetermined control effort aLQR = acceleration due to linear-quadratic-regulatordetermined control effort am = maximum acceleration aobs = acceleration of chaser spacecraft toward an obstacle ax;y;z = accele...

A finite-horizon linear stochastic quadratic optimal control problem is investigated by the GE-evolution operator in sense of mild solution Hilbert spaces. We assume that coefficient differential term a bounded and state input operators are time-varying dynamic equation problem. Optimal feedback along with well-posedness generalized Riccati obtained for case. The results also applicable to ordi...

We describe a recursive formulation of discounted costs for a linear quadratic exponential Gaussian linear regulator problem which implies time-invariant linear decision rules in the innnite horizon case. Time invariance in the discounted case is attained by surrendering state-separability of the risk-adjusted costs.