Article

# Controlling a Class of Nonlinear Systems on Rectangles

Departments of Manuf. & Aerosp. & Mech. Eng., Boston Univ., Brookline, MA

IEEE Transactions on Automatic Control (Impact Factor: 2.72). 12/2006; DOI: 10.1109/TAC.2006.884957 Source: IEEE Xplore

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**ABSTRACT:**In this paper we present a method for automatically generating optimal robot paths satisfying high-level mission specifications. The motion of the robot in the environment is modeled as a weighted transition system. The mission is specified by an arbitrary linear temporal-logic (LTL) formula over propositions satisfied at the regions of a partitioned environment. The mission specification contains an optimizing proposition, which must be repeatedly satisfied. The cost function that we seek to minimize is the maximum time between satisfying instances of the optimizing proposition. For every environment model, and for every formula, our method computes a robot path that minimizes the cost function. The problem is motivated by applications in robotic monitoring and data-gathering. In this setting, the optimizing proposition is satisfied at all locations where data can be uploaded, and the LTL formula specifies a complex data-collection mission. Our method utilizes Büchi automata to produce an automaton (which can be thought of as a graph) whose runs satisfy the temporal-logic specification. We then present a graph algorithm that computes a run corresponding to the optimal robot path. We present an implementation for a robot performing data collection in a road-network platform.The International Journal of Robotics Research 01/2011; 30:1695-1708. · 2.86 Impact Factor - [Show abstract] [Hide abstract]

**ABSTRACT:**Symbolic models have been recently used as a sound mathematical formalism for the formal verification and control design of purely continuous and hybrid systems. In this paper we propose a sequence of symbolic models that approximates a discrete-time Piecewise Affine (PWA) system in the sense of approximate simulation and converges to the PWA system in the so-called simulation metric. Symbolic control design is then addressed with specifications expressed in terms of non-deterministic finite automata. A sequence of symbolic control strategies is derived which converges, in the sense of simulation metric, to the maximal controller solving the given specification on the PWA system.IEEE Transactions on Automatic Control 01/2012; abs/1202.1372. · 2.72 Impact Factor - [Show abstract] [Hide abstract]

**ABSTRACT:**The control-to-facet problem plays an important role in the design of feedback controllers for piecewise-affine hybrid systems on polytopes. In the literature, necessary conditions and sufficient conditions for solvability by static state feedback exist. In this paper, we extend these results to the case of continuous piecewise-affine static output feedback. For the construction of a controller, a triangulation of the output polytope is made which satisfies additional conditions to guarantee compatibility with the induced subdivision of the state polytope. In the state feedback case, the use of this special type of triangulation is not required.IEEE Transactions on Automatic Control 01/2012; 57(11):2831-2843. · 2.72 Impact Factor

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