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. The primary goal is to establish nonconservative, robust, and scalable control theories and algorithms for verifying/achieving desired stability and performance bounds for hybrid affine systems. More specifically, the research activity is 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 digital control of power electronic systems in order to overcome the approximate nature and instability issues suffered by existing approaches to power electronics control.