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

Conference Paper: Safety controller synthesis using human generated trajectories: Nonlinear dynamics with feedback linearization and differential flatness
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ABSTRACT: The aim of the safety controller synthesis problem is to synthesize a feedback controller that results in closedloop trajectories that meet certain criteria, namely, the state or output trajectories terminate in a Goal set without entering an Unsafe set. We propose a formal method for synthesizing such a controller using finitely many human generated trajectories. The main theoretical idea behind our results is the concept of trajectory robustness, which is established using the theory of approximate bisimulation. Approximate bisimulation has been used to establish robustness (in the L∞ sense) of execution trajectories of dynamical systems and hybrid systems, resulting in trajectorybased safety verification procedures. The work reported in this paper builds on our earlier work where the dynamics of the system is assumed to be affine linear. We extend the existing results to special classes of nonlinear dynamical systems, feedback linearizable and differentially flat systems. For both cases, we present some examples where it is possible to synthesize the controller using human generated trajectories, which are obtained through interactive computer programs with graphical interface (computer games).American Control Conference (ACC), 2012; 06/2012  [Show abstract] [Hide abstract]
ABSTRACT: Symbolic models have recently spurred the interest of the research community because they offer a correctbydesign approach to the control of embedded and cyberphysical systems. In this paper we address construction of symbolic models for networks of discretetime nonlinear control systems. The main result of the paper shows that under some small gain theoremtype conditions, a network of symbolic models can be constructed which approximates a network of incrementally stable control systems in the sense of approximate bisimulation with any desired accuracy. Compositional design of quantization parameters of the symbolic models is also derived and based on the topological properties of the network.03/2014;  [Show abstract] [Hide abstract]
ABSTRACT: Motivated by robotic motion planning, we develop a framework for control policy synthesis for both nondeterministic transition systems and Markov decision processes that are subject to temporal logic task specifications. We introduce a fragment of linear temporal logic that can be used to specify common motion planning tasks such as safe navigation, response to the environment, persistent coverage, and surveillance. This fragment is computationally efficient; the complexity of control policy synthesis is a doublyexponential improvement over standard linear temporal logic for both nondeterministic transition systems and Markov decision processes. This improvement is possible because we compute directly on the original system, as opposed to the automatabased approach commonly used. We give simulation results for representative motion planning tasks and compare to generalized reactivity(1).Robotics and Automation (ICRA), 2013 IEEE International Conference on; 01/2013
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