arXiv subjects

Bartolomeo Stellato

Publications and source records attributed to Bartolomeo Stellato.

40 records · Page 3Linked to original sources

arXiv2019

Learning Convex Optimization Control Policies

Many control policies used in various applications determine the input or action by solving a convex optimization problem that depends on the current state and some parameters. Common examples of such convex optimization control policies (COCPs) include the linear quadratic regulator (LQR), convex model predictive control (MPC), and convex control-Lyapunov or approximate dynamic programming (ADP) policies. These types of control policies are tuned by varying the parameters in the optimization problem, such as the LQR weights, to obtain good performance, judged by application-specific metrics. Tuning is often done by hand, or by simple methods such as a crude grid search. In this paper we propose a method to automate this process, by adjusting the parameters using an approximate gradient of the performance metric with respect to the parameters. Our method relies on recently developed methods that can efficiently evaluate the derivative of the solution of a convex optimization problem with respect to its parameters. We illustrate our method on several examples.

math.OC↗

arXiv2016

Second-Order Switching Time Optimization for Switched Dynamical Systems

Switching time optimization arises in finite-horizon optimal control for switched systems where, given a sequence of continuous dynamics, one minimizes a cost function with respect to the switching times. We propose an efficient method for computing the optimal switching times for switched linear and nonlinear systems. A novel second-order optimization algorithm is introduced where, at each iteration, the dynamics are linearized over an underlying time grid to compute the cost function, the gradient and the Hessian efficiently. With the proposed method, the most expensive operations at each iteration are shared between the cost function and its derivatives, thereby greatly reducing the computational burden. We implemented the algorithm in the Julia package SwitchTimeOpt allowing the user to easily solve switching time optimization problems. In the case of linear dynamics, many operations can be further simplified and benchmarks show that our approach is able to provide optimal solutions in just a few ms. In the case of nonlinear dynamics, two examples show that our method provides optimal solutions with up to two orders of magnitude time reductions over state-of-the-art approaches.

math.OC↗

arXiv2016

High-Speed Finite Control Set Model Predictive Control for Power Electronics

Common approaches for direct model predictive control (MPC) for current reference tracking in power electronics suffer from the high computational complexity encountered when solving integer optimal control problems over long prediction horizons. We propose an efficient alternative method based on approximate dynamic programming, greatly reducing the computational burden and enabling sampling times below 25 $μ$s. Our approach is based on the offline estimation of an infinite horizon value function which is then utilized as the tail cost of an MPC problem. This allows us to reduce the controller horizon to a very small number of stages while simultaneously improving the overall controller performance. Our proposed algorithm was implemented on a small size FPGA and validated on a variable speed drive system with a three-level voltage source converter. Time measurements showed that our algorithm requires only 5.76 $μ$s for horizon N = 1 and 17.27 $μ$s for N = 2, in both cases outperforming state of the art approaches with much longer horizons in terms of currents distortion and switching frequency. To the authors' knowledge, this is the first time direct MPC for current control has been implemented on an FPGA solving the integer optimization problem in real-time and achieving comparable performance to formulations with long prediction horizons.

math.OC↗

arXiv2016

Multivariate Chebyshev Inequality with Estimated Mean and Variance

A variant of the well-known Chebyshev inequality for scalar random variables can be formulated in the case where the mean and variance are estimated from samples. In this paper we present a generalization of this result to multiple dimensions where the only requirement is that the samples are independent and identically distributed. Furthermore, we show that as the number of samples tends to infinity our inequality converges to the theoretical multi-dimensional Chebyshev bound.

stat.ME↗