Joao Paulo Jansch-Porto

Joao Paulo Jansch-Porto, Bin Hu, Geir Dullerud

Recently, policy optimization for control purposes has received renewed attention due to the increasing interest in reinforcement learning. In this paper, we investigate the global convergence of gradient-based policy optimization methods for quadratic optimal control of discrete-time Markovian jump linear systems (MJLS). First, we study the optimization landscape of direct policy optimization for MJLS, with static state feedback controllers and quadratic performance costs. Despite the non-convexity of the resultant problem, we are still able to identify several useful properties such as coercivity, gradient dominance, and almost smoothness. Based on these properties, we show global convergence of three types of policy optimization methods: the gradient descent method; the Gauss-Newton method; and the natural policy gradient method. We prove that all three methods converge to the optimal state feedback controller for MJLS at a linear rate if initialized at a controller which is mean-square stabilizing. Some numerical examples are presented to support the theory. This work brings new insights for understanding the performance of policy gradient methods on the Markovian jump linear quadratic control problem.

Joao Paulo Jansch-Porto, Bin Hu, Geir Dullerud

Markovian jump linear systems (MJLS) are an important class of dynamical systems that arise in many control applications. In this paper, we introduce the problem of controlling unknown (discrete-time) MJLS as a new benchmark for policy-based reinforcement learning of Markov decision processes (MDPs) with mixed continuous/discrete state variables. Compared with the traditional linear quadratic regulator (LQR), our proposed problem leads to a special hybrid MDP (with mixed continuous and discrete variables) and poses significant new challenges due to the appearance of an underlying Markov jump parameter governing the mode of the system dynamics. Specifically, the state of a MJLS does not form a Markov chain and hence one cannot study the MJLS control problem as a MDP with solely continuous state variable. However, one can augment the state and the jump parameter to obtain a MDP with a mixed continuous/discrete state space. We discuss how control theory sheds light on the policy parameterization of such hybrid MDPs. Then we modify the widely used natural policy gradient method to directly learn the optimal state feedback control policy for MJLS without identifying either the system dynamics or the transition probability of the switching parameter. We implement the (data-driven) natural policy gradient method on different MJLS examples. Our simulation results suggest that the natural gradient method can efficiently learn the optimal controller for MJLS with unknown dynamics.

Joao Paulo Jansch-Porto, Bin Hu, Geir Dullerud

Recently, policy optimization for control purposes has received renewed attention due to the increasing interest in reinforcement learning. In this paper, we investigate the convergence of policy optimization for quadratic control of Markovian jump linear systems (MJLS). First, we study the optimization landscape of direct policy optimization for MJLS, and, in particular, show that despite the non-convexity of the resultant problem the unique stationary point is the global optimal solution. Next, we prove that the Gauss-Newton method and the natural policy gradient method converge to the optimal state feedback controller for MJLS at a linear rate if initialized at a controller which stabilizes the closed-loop dynamics in the mean square sense. We propose a novel Lyapunov argument to fix a key stability issue in the convergence proof. Finally, we present a numerical example to support our theory. Our work brings new insights for understanding the performance of policy learning methods on controlling unknown MJLS.

Ritwika Ghosh, Joao P. Jansch-Porto, Chiao Hsieh et al.

Programming languages, libraries, and development tools have transformed the application development processes for mobile computing and machine learning. This paper introduces the CyPhyHouse - a toolchain that aims to provide similar programming, debugging, and deployment benefits for distributed mobile robotic applications. Users can develop hardware-agnostic, distributed applications using the high-level, event driven Koord programming language, without requiring expertise in controller design or distributed network protocols. The modular, platform-independent middleware of CyPhyHouse implements these functionalities using standard algorithms for path planning (RRT), control (MPC), mutual exclusion, etc. A high-fidelity, scalable, multi-threaded simulator for Koord applications is developed to simulate the same application code for dozens of heterogeneous agents. The same compiled code can also be deployed on heterogeneous mobile platforms. The effectiveness of CyPhyHouse in improving the design cycles is explicitly illustrated in a robotic testbed through development, simulation, and deployment of a distributed task allocation application on in-house ground and aerial vehicles.