I t is shown that the calculation of the performance of a class of suboptimal linear control systems is similar to the calculation of the performance of an equivalent optimal system. The performances of both optimal and suboptimal linear systems have terms for cost owing to uncertainty about the initial state of the plant, a nonzero mean of the initial state, error in the estimate of the state,...

We prove upper and lower bounds relating the quantum gate complexity of a unitary operation, U, to the optimal control cost associated to the synthesis of U. These bounds apply for any optimal control problem, and can be used to show that the quantum gate complexity is essentially equivalent to the optimal control cost for a wide range of problems, including time-optimal control and finding min...

We present a method for the solution of the Dynamic Programming Equation (DPE) that arises in an infinite horizon optimal control problem. The method extends to the discrete time version of Al’brecht’s procedure for locally approximating the solution of the Hamilton Jacobi Bellman PDE. Assuming that the dynamics and cost are C(R) and C(R) smooth, respectively, we explicitly find expansions of t...

The research on time optimal control problems dates back to the 1960’s. Issues such as existence, necessary conditions for optimality and controllability have been discussed. We refer the reader to [6] for the finite dimensional case, and to [1, 4, 7, 9] for the infinite dimensional case. The cost functional for a time optimal control problem is the infimum of a number set. On the other hand, t...

In this study of the nonlinear H∞-optimal control design for strict-feedback nonlinear systems our objective is to construct globally stabilizing control laws to match the optimal control law up to any desired order, and to be inverse optimal with respect to some computable cost functional. Our recursive construction of a cost functional and the corresponding solution to the Hamilton-Jacobi-Isa...

This article introduces a generalization of problems in the domain of the optimal control of quantum systems viz. costs imposed on impulsive and bounded controls for quantum spin systems with drift. The dynamic programming approach from optimal control is used to analyze the former, and the discontinuous nature of the optimal cost function is used to motivate the need for an interpretation in t...

We propose an optimal control approach to robust control design. Our goal is to design a state feedback to stabilize a system under uncertainty. We translate this robust control problem into an optimal control problem of minimizing a cost. Because the uncertainty bound is reeected in the cost, the solution to the optimal control problem is a solution to the robust control problem. Our approach ...

This paper proposes an Optimal Power Flow (OPF) algorithm by Direct Load Control (DLC) programs to optimize the operational cost of smart grids considering various scenarios based on different constraints. The cost function includes active power production cost of available power sources and a novel flexible load curtailment cost associated with DLC programs. The load curtailment cost is based ...

We consider critically loaded single class queueing networks with infinite buffers in which arrival and service rates are state (i.e., queue length) dependent and may be dynamically controlled. An optimal rate control problem for such networks with an ergodic cost criterion is studied. It is shown that the value function (i.e., optimum value of the cost) of the rate control problem for the netw...

We consider critically loaded single class queueing networks with infinite buffers in which arrival and service rates are state (i.e., queue length) dependent and may be dynamically controlled. An optimal rate control problem for such networks with an ergodic cost criterion is studied. It is shown that the value function (i.e., optimum value of the cost) of the rate control problem for the netw...