Convex Chance Constrained Model Predictive Control

We consider the Chance Constrained Model Predictive Control problem for polynomial systems subject to disturbances. In this problem, we aim at finding optimal control input for given disturbed dynamical system to minimize a given cost function subject to probabilistic constraints, over a finite horizon. The control laws provided have a predefined (low) risk of not reaching the desired target set. Building on the theory of measures and moments, a sequence of finite semidefinite programmings are provided, whose solution is shown to converge to the optimal solution of the original problem. Numerical examples are presented to illustrate the computational performance of the proposed approach.Comment: This work has been submitted to the 55th IEEE Conference on Decision and Contro

Reconstruction of Support of a Measure From Its Moments

In this paper, we address the problem of reconstruction of support of a measure from its moments. More precisely, given a finite subset of the moments of a measure, we develop a semidefinite program for approximating the support of measure using level sets of polynomials. To solve this problem, a sequence of convex relaxations is provided, whose optimal solution is shown to converge to the support of measure of interest. Moreover, the provided approach is modified to improve the results for uniform measures. Numerical examples are presented to illustrate the performance of the proposed approach.Comment: This has been submitted to the 53rd IEEE Conference on Decision and Contro

Moment-Sum-Of-Squares Approach For Fast Risk Estimation In Uncertain Environments

In this paper, we address the risk estimation problem where one aims at estimating the probability of violation of safety constraints for a robot in the presence of bounded uncertainties with arbitrary probability distributions. In this problem, an unsafe set is described by level sets of polynomials that is, in general, a non-convex set. Uncertainty arises due to the probabilistic parameters of the unsafe set and probabilistic states of the robot. To solve this problem, we use a moment-based representation of probability distributions. We describe upper and lower bounds of the risk in terms of a linear weighted sum of the moments. Weights are coefficients of a univariate Chebyshev polynomial obtained by solving a sum-of-squares optimization problem in the offline step. Hence, given a finite number of moments of probability distributions, risk can be estimated in real-time. We demonstrate the performance of the provided approach by solving probabilistic collision checking problems where we aim to find the probability of collision of a robot with a non-convex obstacle in the presence of probabilistic uncertainties in the location of the robot and size, location, and geometry of the obstacle.Comment: 57th IEEE Conference on Decision and Control 201

Chance-constrained sets approximation: A probabilistic scaling approach

In this paper, a sample-based procedure for obtaining simple and computable approximations of chance-constrained sets is proposed. The procedure allows to control the complexity of the approximating set, by defining families of simple-approximating sets of given complexity. A probabilistic scaling procedure then scales these sets to obtain the desired probabilistic guarantees. The proposed approach is shown to be applicable in several problems in systems and control, such as the design of Stochastic Model Predictive Control schemes or the solution of probabilistic set membership estimation problems

Stochastic MPC Design for a Two-Component Granulation Process

We address the issue of control of a stochastic two-component granulation process in pharmaceutical applications through using Stochastic Model Predictive Control (SMPC) and model reduction to obtain the desired particle distribution. We first use the method of moments to reduce the governing integro-differential equation down to a nonlinear ordinary differential equation (ODE). This reduced-order model is employed in the SMPC formulation. The probabilistic constraints in this formulation keep the variance of particles' drug concentration in an admissible range. To solve the resulting stochastic optimization problem, we first employ polynomial chaos expansion to obtain the Probability Distribution Function (PDF) of the future state variables using the uncertain variables' distributions. As a result, the original stochastic optimization problem for a particulate system is converted to a deterministic dynamic optimization. This approximation lessens the computation burden of the controller and makes its real time application possible.Comment: American control Conference, May, 201

Experience Transfer for Robust Direct Data-Driven Control

Learning-based control uses data to design efficient controllers for specific systems. When multiple systems are involved, experience transfer usually focuses on data availability and controller performance yet neglects robustness to variations between systems. In contrast, this letter explores experience transfer from a robustness perspective. We leverage the transfer to design controllers that are robust not only to the uncertainty regarding an individual agent's model but also to the choice of agent in a fleet. Experience transfer enables the design of safe and robust controllers that work out of the box for all systems in a heterogeneous fleet. Our approach combines scenario optimization and recent formulations for direct data-driven control without the need to estimate a model of the system or determine uncertainty bounds for its parameters. We demonstrate the benefits of our data-driven robustification method through a numerical case study and obtain learned controllers that generalize well from a small number of open-loop trajectories in a quadcopter simulation