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A step-search sequential quadratic programming method is proposed for solving nonlinear equality constrained stochastic optimization problems. It is assumed that constraint function values and derivatives are available, but only stochastic…
This paper proposes a new sampling-based nonlinear model predictive control (MPC) algorithm, with a bound on complexity quadratic in the prediction horizon N and linear in the number of samples. The idea of the proposed algorithm is to use…
Multidisciplinary engineering system design typically employs a sequential process, progressing from system dynamics to design variables and control. However, this process is inefficient and may lead to a suboptimal design. We propose…
Piecewise constant control approximation provides a practical framework for designing numerical schemes of continuous-time control problems. We analyze the accuracy of such approximations for extended mean field control (MFC) problems,…
Efficient Riccati equation based techniques for the approximate solution of discrete time linear regulator problems are restricted in their application to problems with quadratic terminal payoffs. Where non-quadratic terminal payoffs are…
A time-inconsistent optimal control problem is formulated and studied for a controlled linear ordinary differential equation with quadratic cost functional. A notion of equilibrium control is introduced, which can be regarded as a…
This paper focuses on finding approximate solutions to stochastic optimal control problems with control domains being not necessarily convex, where the state trajectory is subject to controlled stochastic differential equations. The…
We propose an approach to trajectory optimization for piecewise polynomial systems based on the recently proposed graphs of convex sets framework. We instantiate the framework with a convex relaxation of optimal control based on occupation…
The recently introduced harmonic resolvent framework is concerned with the study of the input-output dynamics of nonlinear flows in the proximity of a known time-periodic orbit. These dynamics are governed by the harmonic resolvent…
We introduce a new iterative method for computing solutions of elliptic equations with random rapidly oscillating coefficients. Similarly to a multigrid method, each step of the iteration involves different computations meant to address…
This paper is devoted to the a posteriori error analysis of multiharmonic finite element approximations to distributed optimal control problems with time-periodic state equations of parabolic type. We derive a posteriori estimates of…
The state-of-the-art in optimal control from timed temporal logic specifications, including Metric Temporal Logic (MTL) and Signal Temporal Logic (STL), is based on Mixed-Integer Convex Programming (MICP). The standard MICP approach is…
We present a numerical method to compute expectations of functionals of a piecewise-deterministic Markov process. We discuss time dependent functionals as well as deterministic time horizon problems. Our approach is based on the…
We consider the null controllability problem for the wave equation, and analyse a stabilized finite element method formulated on a global, unstructured spacetime mesh. We prove error estimates for the approximate control given by the…
We study a multi-period convex quadratic optimization problem, where the state evolves dynamically as an affine function of the state, control, and indicator variables in each period. We begin by projecting out the state variables using…
A finite horizon linear quadratic(LQ) optimal control problem is studied for a class of discrete-time linear fractional systems (LFSs) affected by multiplicative, independent random perturbations. Based on the dynamic programming technique,…
The minimization of energy-like cost functionals is addressed in the context of optimal control problems. For a general class of dynamical systems, with possibly unstable and nonlinear free dynamics, it is shown that a sequence of solutions…
We introduce a new and efficient numerical method for multicriterion optimal control and single criterion optimal control under integral constraints. The approach is based on extending the state space to include information on a "budget"…
In this work, we found a non trivial topology to achieve the controllability for linear and nonlinear system in finite or infinite time horizon. We give several examples illustrating this topologizing method for the controllability results.…
We study the problem of minimizing a nonnegative separable concave function over a compact feasible set. We approximate this problem to within a factor of 1+epsilon by a piecewise-linear minimization problem over the same feasible set. Our…