Humberto Gonzalez

Provably safe and robust learning-based model predictive control

Controller design faces a trade-off between robustness and performance, and the reliability of linear controllers has caused many practitioners to focus on the former. However, there is renewed interest in improving system performance to deal with growing energy constraints. This paper describes a learning-based model predictive control (LBMPC) scheme that provides deterministic guarantees on robustness, while statistical identification tools are used to identify richer models of the system in order to improve performance; the benefits of this framework are that it handles state and input constraints, optimizes system performance with respect to a cost function, and can be designed to use a wide variety of parametric or nonparametric statistical tools. The main insight of LBMPC is that safety and performance can be decoupled under reasonable conditions in an optimization framework by maintaining two models of the system. The first is an approximate model with bounds on its uncertainty, and the second model is updated by statistical methods. LBMPC improves performance by choosing inputs that minimize a cost subject to the learned dynamics, and it ensures safety and robustness by checking whether these same inputs keep the approximate model stable when it is subject to uncertainty. Furthermore, we show that if the system is sufficiently excited, then the LBMPC control action probabilistically converges to that of an MPC computed using the true dynamics.

Real-Time Wireless Sensor-Actuator Networks for Industrial Cyber-Physical Systems

With recent adoption of wireless sensor-actuator networks (WSANs) in industrial automation, industrial wireless control systems have emerged as a frontier of cyber-physical systems. Despite their success in industrial monitoring applications, existing WSAN technologies face significant challenges in supporting control systems due to their lack of real-time performance and dynamic wireless conditions in industrial plants. This article reviews a series of recent advances in real-time WSANs for industrial control systems: 1) real-time scheduling algorithms and analyses for WSANs; 2) implementation and experimentation of industrial WSAN protocols; 3) cyber-physical codesign of wireless control systems that integrate wireless and control designs; and 4) a wireless cyber-physical simulator for codesign and evaluation of wireless control systems. This article concludes by highlighting research directions in industrial cyber-physical systems.

A descent algorithm for the optimal control of constrained nonlinear switched dynamical systems

One of the oldest problems in the study of dynamical systems is the calculation of an optimal control. Though the determination of a numerical solution for the general non-convex optimal control problem for hybrid systems has been pursued relentlessly to date, it has proven difficult, since it demands nominal mode scheduling. In this paper, we calculate a numerical solution to the optimal control problem for a constrained switched nonlinear dynamical system with a running and final cost. The control parameter has a discrete component, the sequence of modes, and two continuous components, the duration of each mode and the continuous input while in each mode. To overcome the complexity posed by the discrete optimization problem, we propose a bi-level hierarchical optimization algorithm: at the higher level, the algorithm updates the mode sequence by using a single-mode variation technique, and at the lower level, the algorithm considers a fixed mode sequence and minimizes the cost functional over the continuous components. Numerical examples detail the potential of our proposed methodology.

A numerical method for the optimal control of switched systems

Switched dynamical systems have shown great utility in modeling a variety of systems. Unfortunately, the determination of a numerical solution for the optimal control of such systems has proven difficult, since it demands optimal mode scheduling. Recently, we constructed an optimization algorithm to calculate a numerical solution to the problem subject to a running and final cost. In this paper, we modify our original approach in three ways to make our algorithms application more tenable. First, we transform our algorithm to allow it to begin at an infeasible point and still converge to a lower cost feasible point. Second, we incorporate multiple objectives into our cost function, which makes the development of an optimal control in the presence of multiple goals viable. Finally, we extend our approach to penalize the number of hybrid jumps. We also detail the utility of these extensions to our original approach by considering two examples.

Incorporating emergency alarms in reliable wireless process control

Recent years have witnessed adoption of wireless sensor-actuator networks (WSANs) in process control. Many real-world process control systems must handle various emergency alarms under stringent timing constraints in addition to regular control loops. However, despite considerable theoretical results on wireless control, the problem of incorporating emergency alarms in wireless control has received little attention. This paper presents, to the best of our knowledge, the first systematic approach to incorporate emergency alarms into wireless process control. The challenge in emergency communication lies in the fact that emergencies occur occasionally, but must be delivered within their deadlines when they occur. The contributions of this work are three-fold: (1) we propose efficient real-time emergency communication protocols based on slot stealing and event-based communication; (2) we build an open-source WirelessHART protocol stack in the Wireless Cyber-Physical Simulator (WCPS) for holistic simulations of wireless control systems; (3) we conduct systematic studies on a coupled water tank system controlled over a 6-hop 21-node WSAN. Our results demonstrate our real-time emergency communication approach enables timely emergency handling, while allowing regular feedback control loops to effectively share resources in WSANs during normal operations.

Model-based design: a report from the trenches of the DARPA Urban Challenge

The impact of model-based design on the software engineering community is impressive, and recent research in model transformations, and elegant behavioral specifications of systems has the potential to revolutionize the way in which systems are designed. Such techniques aim to raise the level of abstraction at which systems are specified, to remove the burden of producing application-specific programs with general-purpose programming. For complex real-time systems, however, the impact of model-driven approaches is not nearly so widespread. In this paper, we present a perspective of model-based design researchers who joined with software experts in robotics to enter the DARPA Urban Challenge, and to what extent model-based design techniques were used. Further, we speculate on why, according to our experience and the testimonies of many teams, the full promises of model-based design were not widely realized for the competition. Finally, we present some thoughts for the future of model-based design in complex systems such as these, and what advancements in modeling are needed to motivate small-scale projects to use model-based design in these domains.

Consistent Approximations for the Optimal Control of Constrained Switched Systems---Part 2: An Implementable Algorithm

In the first part of this two-paper series, we presented a conceptual algorithm for the optimal control of constrained switched systems and proved that this algorithm generates a sequence of points...

Metrization and Simulation of Controlled Hybrid Systems

The study of controlled hybrid systems requires practical tools for approximation and comparison of system behaviors. Existing approaches to these problems impose undue restrictions on the systems continuous and discrete dynamics. Metrization and simulation of controlled hybrid systems is considered here in a unified framework by constructing a state space metric. The metric is applied to develop a numerical simulation algorithm that converges uniformly, with a known rate of convergence, to orbitally stable executions of controlled hybrid systems, up to and including Zeno events. Benchmark hybrid phenomena illustrate the utility of the proposed tools.

Wireless routing and control: a cyber-physical case study

Wireless sensor-actuator networks (WSANs) are being adopted in process industries because of their advantages in lowering deployment and maintenance costs. While there has been significant theoretical advancement in networked control design, only limited empirical results that combine control design with realistic WSAN standards exist. This paper presents a cyber-physical case study on a wireless process control system that integrates state-of-the-art network control design and a WSAN based on the WirelessHART standard. The case study systematically explores the interactions between wireless routing and control design in the process control plant. The network supports alternative routing strategies, including single-path source routing and multi-path graph routing. To mitigate the effect of data loss in the WSAN, the control design integrates an observer based on an Extended Kalman Filter with a model predictive controller and an actuator buffer of recent control inputs. We observe that sensing and actuation can have different levels of resilience to packet loss under this network control design. We then propose a flexible routing approach where the routing strategy for sensing and actuation can be configured separately. Finally, we show that an asymmetric routing configuration with different routing strategies for sensing and actuation can effectively improve control performance under significant packet loss. Our results highlight the importance of co- joining the design of wireless network protocols and control in wireless control systems.

Numerical integration of hybrid dynamical systems via domain relaxation

Though hybrid dynamical systems are a powerful modeling tool, it has proven difficult to accurately simulate their trajectories. In this paper, we develop a provably convergent numerical integration scheme for approximating trajectories of hybrid dynamical systems. This is accomplished by first relaxing hybrid systems whose continuous states reside on manifolds by attaching epsilon-sized strips to portions of the boundary and then extending the dynamic and distance metric onto these strips. On this space we develop a numerical integration scheme and prove that discrete approximations converge to trajectories of the hybrid system. An example is included to illustrate the approach.