Related papers: Turnpike and dissipativity in generalized discrete…
The investigation of optimal processes has a long history in the field of thermodynamics. It is well known that finite-time processes that minimize dissipation often exhibit discontinuities. We use a combination of numerical and analytical…
This paper presents analyses for the maximum hands-off control using the geometric methods developed for the theory of turnpike in optimal control. First, a sufficient condition is proved for the existence of the maximum hands-off control…
We consider a variant of the classical linear quadratic Gaussian regulator (LQG) in which penalties on the endpoint state are replaced by the specification of the terminal state distribution. The resulting theory considerably differs from…
We study the optimal control of discrete time mean filed dynamical systems under partial observations. We express the global law of the filtered process as a controlled system with its own dynamics. Following a dynamic programming approach,…
This work considers stochastic operators in general inner-product spaces, and in particular, systems with stochastically time-varying input delays of a known probability distribution. Stochastic dissipativity and stability are defined from…
In this paper, we study the optimal control of a discrete-time stochastic differential equation (SDE) of mean-field type, where the coefficients can depend on both a function of the law and the state of the process. We establish a new…
In this paper, we establish an exponential periodic turnpike property for linear quadratic optimal control problems governed by periodic systems in infinite dimension. We show that the optimal trajectory converges exponentially to a…
Model Predictive Control (MPC) is well understood in the deterministic setting, yet rigorous stability and performance guarantees for stochastic MPC remain limited to the consideration of terminal constraints and penalties. In contrast,…
We present a new proof of the turnpike property for nonlinear optimal control problems, when the running target is a steady control-state pair of the underlying system. Our strategy combines the construction of quasi-turnpike controls via…
This work is concerned with the exponential turnpike property for optimal control problems of particle systems and their mean-field limit. Under the assumption of the strict dissipativity of the cost function, exponential estimates for both…
This work addresses the optimal covariance control problem for stochastic discrete-time linear time-varying systems subject to chance constraints. Covariance steering is a stochastic control problem to steer the system state Gaussian…
In this paper, we introduce turnpike arguments in the context of optimal state estimation. In particular, we show that the optimal solution of the state estimation problem involving all available past data serves as turnpike for the…
This paper studies the problem of steering the distribution of a discrete-time dynamical system from an initial distribution to a target distribution in finite time. The formulation is fully nonlinear, allowing the use of general control…
We consider a class of stochastic optimal control problems for discrete-time stochastic linear systems which seek for control policies that will steer the probability distribution of the terminal state of the system close to a desired…
Optimal control problems with symmetries often admit a non stationary turnpike property called trim turnpike, which characterizes the convergence of optimal solutions to certain symmetry induced trajectories called trim primitives. In this…
We consider averages convergence as the time-horizon goes to infinity of optimal solutions of time-dependent optimal control problems to optimal solutions of the corresponding stationary optimal control problems. Control problems play a key…
We consider the problem of minimizing the supplied energy of infinite-dimensional linear port-Hamiltonian systems and prove that optimal trajectories exhibit the turnpike phenomenon towards certain subspaces induced by the dissipation of…
We present stability conditions for deterministic time-varying nonlinear discrete-time systems whose inputs aim to minimize an infinite-horizon time-dependent cost. Global asymptotic and exponential stability properties for general…
In this paper the turnpike property is established for a non-convex optimal control problem in discrete time. The functional is defined by the notion of the ideal convergence and can be considered as an analogue of the terminal functional…
Inspired by the successes of stochastic algorithms in the training of deep neural networks and the simulation of interacting particle systems, we propose and analyze a framework for randomized time-splitting in linear-quadratic optimal…