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Many real-world systems often involve physical components or operating environments with highly nonlinear and uncertain dynamics. A number of different control algorithms can be used to design optimal controllers for such systems, assuming…

Dual control denotes a class of control problems where the parameters governing the system are imperfectly known. The challenge is to find the optimal balance between probing, i.e. exciting the system to understand it more, and caution,…

Achieving both optimality and safety under unknown system dynamics is a central challenge in real-world deployment of agents. To address this, we introduce a notion of maximum safe dynamics learning, where sufficient exploration is…

Stochastic maximum principle of nonlinear controlled forward-backward systems, where the set of strict (classical) controls need not be convex and the diffusion coefficient depends explicitly on the variable control, is an open problem…

Uncertainties arising in various control systems, such as robots that are subject to unknown disturbances or environmental variations, pose significant challenges for ensuring system safety, such as collision avoidance. At the same time,…

Control of systems operating in unexplored environments is challenging due to lack of complete model knowledge. Additionally, under measurement noises, data collected from onboard sensors are of limited accuracy. This paper considers…

Here and in a follow-on paper, we consider a simple control problem in which the underlying dynamics depend on a parameter $a$ that is unknown and must be learned. In this paper, we assume that $a$ is bounded, i.e., that $|a| \le…

The deformable and continuum nature of soft robots promises versatility and adaptability. However, control of modular, multi-limbed soft robots for terrestrial locomotion is challenging due to the complex robot structure, actuator mechanics…

This paper studies (single-time and multitime) optimal control problems on a nonholonomic manifold (described either by the kernel of a Gibbs-Pfaff form or by the span of appropriate vector fields). For both descriptions we analyse:…

We present a multilevel stochastic gradient descent method for the optimal control of systems governed by partial differential equations under uncertain input data. The gradient descent method used to find the optimal control leverages a…

We propose a method of bi-coordinate variations for non-stationary and non-smooth optimization problems, which involve a single linear equality and box constraints. Here only approximation sequences are known instead of exact values of the…

Design of robots at the small scale is a trial-and-error based process, which is costly and time-consuming. There are few dynamic simulation tools available to accurately predict the motion or performance of untethered microrobots as they…

This paper studies continuous-time stochastic control problems whose controlled states are fully non-Markovian and depend on unknown model parameters. Such problems arise naturally in path-dependent stochastic differential equations,…

The energetic optimization problem, e.g., searching for the optimal switch- ing protocol of certain system parameters to minimize the input work, has been extensively studied by stochastic thermodynamics. In current work, we study this…

This paper presents an approach to deal with safety of dynamical systems in presence of multiple non-convex unsafe sets. While optimal control and model predictive control strategies can be employed in these scenarios, they suffer from high…

This paper deals with the problems of stochastic stability and sliding mode control for a class of continuous-time Markovian jump systems with mode-dependent time-varying delays and partly unknown transition probabilities. The design method…

For a broad class of nonlinear systems, we formulate the problem of guaranteeing safety with optimality under constraints. Specifically, we define controlled safety for differential inclusions with constraints on the states and the inputs.…

This work develops an efficient and accurate optimization algorithm to study the optimal mixing problem driven by boundary control of unsteady Stokes flows, based on the theoretical foundation laid by Hu and Wu in a series of work. The…

This paper presents a control framework that combines model-based optimal control and reinforcement learning (RL) to achieve versatile and robust legged locomotion. Our approach enhances the RL training process by incorporating on-demand…

We present an optimization-based method to plan the motion of an autonomous robot under the uncertainties associated with dynamic obstacles, such as humans. Our method bounds the marginal risk of collisions at each point in time by…