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We construct a finite element like scheme for fully non-linear integro-partial differential equations arising in optimal control of jump-processes. Special cases of these equations include optimal portfolio and option pricing equations in…
The paper is devoted to the study of a new class of optimal control problems for nonsmooth dynamical systems governed by nonconvex discontinuous differential inclusions of the sweeping type with involving variable time into optimization. We…
We address the tracking problem for a class of uncertain non-affine nonlinear systems with high relative degrees, performing non-repetitive tasks. We propose a rigorously proven, robust adaptive learning control scheme that relies on a…
In this paper, we study probabilistic numerical methods based on optimal quantization algorithms for computing the solution to optimal multiple switching problems with regime-dependent state process. We first consider a discrete-time…
In this paper, we consider multistopping problems for finite discrete time sequences $X_1,...,X_n$. $m$-stops are allowed and the aim is to maximize the expected value of the best of these $m$ stops. The random variables are neither assumed…
We present the conditions under which the time-optimal control problem for a nonlinear non-autonomous linearizable system can be solved by the method of successive approximations, at each step of which a power Markov moment min-problem is…
We consider the problem of optimal multiple switching in finite horizon, when the state of the system, including the switching costs, is a general adapted stochastic process. The problem is formulated as an extended impulse control problem…
This paper presents the jump law of co-states in optimal control for state-dependent switched systems. The number of switches and the switching modes are assumed to be known a priori. A proposed jump law is rigorously derived by theoretical…
We introduce a notion of bounded variation solution for a new class of nonlinear control systems with ordinary and impulsive controls, in which the drift function depends not only on the state, but also on its past history, through a finite…
We introduce a family of hybrid discretisations for the numerical approximation of optimal control problems governed by the equations of immiscible displacement in porous media. The proposed schemes are based on mixed and discontinuous…
In this paper, we obtain the maximum principle for optimal controls of stochastic systems with jumps by introducing a new method of variation. The control is allowed to enter both diffusion and jump term and the control domain need not to…
This work presents an algorithmic scheme for solving the infinite-time constrained linear quadratic regulation problem. We employ an accelerated version of a popular proximal gradient scheme, commonly known as the Forward-Backward Splitting…
We pose the approximation problem for scalar nonnegative input-output systems via impulse response convolutions of finite order, i.e. finite order moving averages, based on repeated observations of input/output signal pairs. The problem is…
Switching-constrained optimization problems form a difficult class of mathematical programs since their feasible set is almost disconnected while standard constraint qualifications are likely to fail at several feasible points. That is why…
This paper presents a stochastic model predictive control approach for nonlinear systems subject to time-invariant probabilistic uncertainties in model parameters and initial conditions. The stochastic optimal control problem entails a cost…
This paper deals with design of maximum hands-off hybrid control sequences for discrete-time switched linear systems. It is a sparsest combination of a discrete control sequence (i.e. the switching sequence) and a continuous control…
In this paper, we study numerical approximations for optimal control of a class of stochastic partial differential equations with partial observations. The system state evolves in a Hilbert space, whereas observations are given in…
In this paper, we propose a new control design scheme for solving the obstacle avoidance problem for nonlinear driftless control-affine systems. The class of systems under consideration satisfies controllability conditions with iterated Lie…
Efficient trajectory generation is crucial for autonomous systems; however, current numerical methods often struggle to handle periodic behaviors effectively, particularly when the onboard sensors require equidistant temporal sampling. This…
We prove convergence of the proximal policy gradient method for a class of constrained stochastic control problems with control in both the drift and diffusion of the state process. The problem requires either the running or terminal cost…