Digital Control of Hybrid Systems via Simulation and Bisimulation

Abstract:

The research objective of this project is to bridge two disparate paths to the control of hybrid dynamical systems—namely, symbolic model-based and Lyapunov analysis-based approaches—via convex programming in order to address major challenges in hybrid control. Hybrid systems are characterized by the presence of both continuous dynamics and discrete logic that interact with each other. Many engineering systems today are hybrid because digital computers, communication networks, and electronic circuits are often integral parts of the overall system. In particular, piecewise affine systems comprise an important class of hybrid systems that are relatively tractable models of nonlinear systems. Yet control problems for such models are of combinatorial complexity, and existing theories are inherently conservative (i.e., based on conditions that are sufficient but not necessary) or lack scalability (i.e., the ability to trade off performance against computational cost). The primary goal of this project is to establish nonconservative, robust, and scalable control theories and algorithms for verifying/achieving desired stability and performance bounds for hybrid affine systems. The PIs will reach this goal by making substantial advances in cyber- physical systems research.

More specifically, the research activity will be focused on making the following advances:

(a) A tightly drawn, nested sequence of finite-state symbolic models that simulate, or cover the behavior of, the controlled piecewise affine model will be discovered, so that the sequence either converges to the true hybrid model, or is finite and results in a finite-state bisimulation which is equivalent to the true model.

(b) Through Lyapunov analysis and convex programming, each of these symbolic models will be associated with a controller synthesis algorithm, so that the control designer always has the option to either settle for a given controller synthesis, or go down the sequence of symbolic models further and obtain a potentially better controller synthesis in return for more computational cost paid;

(c) For practical applicability, the presence of uncertainty (e.g., unknown disturbances and modeling errors) will be taken into account within the symbolic models, so that the resulting controllers will be robust against uncertainty; and

(d) The developed theories and algorithms will be applied to power electronic systems in order to overcome the approximate nature and instability issues suffered by existing approaches to power electronics control. A significant component of this task is the creation of a custom-design digital control system consisting of a Field Programmable Gate Array (FPGA) and microprocessor. The FPGA is used to implement a control algorithm synthesized by the microprocessor. Along with high-speed Analog/Digital (A/D) Converters, the FPGA implementation enables control update rates significantly faster than switching rate of power transistors, and so switching instances can be adjusted based upon new data. The microprocessor, a dual-core Intel i5 processor operating at 3.6GHz, will be used to synthesize an optimal control algorithm.