375 research outputs found

    Receding-horizon switched linear system design: a semidefinite programming approach with distributed computation

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    This dissertation presents a framework for analysis and controller synthesis problems for switched linear systems. These are multi-modal systems whose parameters vary within a finite set according to the state of a discrete time automaton; the switching signal may be unconstrained or may be drawn from a language of admissible switching signals. This model of system dynamics and discrete logic has many applications in a number of engineering contexts. A receding-horizon type approach is taken by designing controllers with access to a finite-length preview of future modes and finite memory of past modes; the length of both preview and memory are taken as design choices. The results developed here take the form of nested sequences of SDP feasibility problems. These conditions are exact in that the feasibility of any element of the sequence is sufficient to construct a suitable controller, while the existence of a suitable controller necessitates the feasibility of some element of the sequence. Considered first is the problem of controller synthesis for the stabilization of switched systems. These developments serve both as a control problem of interest and a demonstration of the methods used to solve subsequent switched control problems. Exact conditions for the existence of a controller are developed, along with converse results which rule out levels of closed-loop stability based on the infeasibility of individual SDP problems. This permits the achievable closed-loop performance level to be approximated to arbitrary accuracy. Examined next are two different performance problems: one of disturbance attenuation and one of windowed variance. For each problem, controller synthesis conditions are presented exactly in the form of SDP feasibility problems which may be optimized to determine levels of performance. In both cases, the performance level may be taken as uniform or allowed to vary based on the switching path encountered. The controller synthesis conditions presented here can grow both large and computationally intensive, but they share a common structural sparsity which may be exploited. The last part of this dissertation examines this structure and presents a distributed approach to solving such problems. This maintains the tractability of these results even at large scales, expanding the scope of systems to which these methods can be applied

    Benelux meeting on systems and control, 23rd, March 17-19, 2004, Helvoirt, The Netherlands

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    Converse Lyapunov theorems for discrete-time linear switching systems with regular switching sequences

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    We present a stability analysis framework for the general class of discrete-time linear switching systems for which the switching sequences belong to a regular language. They admit arbitrary switching systems as special cases. Using recent results of X. Dai on the asymptotic growth rate of such systems, we introduce the concept of multinorm as an algebraic tool for stability analysis. We conjugate this tool with two families of multiple quadratic Lyapunov functions, parameterized by an integer T >= 1, and obtain converse Lyapunov Theorems for each. Lyapunov functions of the first family associate one quadratic form per state of the automaton defining the switching sequences. They are made to decrease after every T successive time steps. The second family is made of the path-dependent Lyapunov functions of Lee and Dullerud. They are parameterized by an amount of memory (T-1) >= 0. Our converse Lyapunov theorems are finite. More precisely, we give sufficient conditions on the asymptotic growth rate of a stable system under which one can compute an integer parameter T >= 1 for which both types of Lyapunov functions exist. As a corollary of our results, we formulate an arbitrary accurate approximation scheme for estimating the asymptotic growth rate of switching systems with constrained switching sequences

    DECENTRALIZED ROBUST NONLINEAR MODEL PREDICTIVE CONTROLLER FOR UNMANNED AERIAL SYSTEMS

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    The nonlinear and unsteady nature of aircraft aerodynamics together with limited practical range of controls and state variables make the use of the linear control theory inadequate especially in the presence of external disturbances, such as wind. In the classical approach, aircraft are controlled by multiple inner and outer loops, designed separately and sequentially. For unmanned aerial systems in particular, control technology must evolve to a point where autonomy is extended to the entire mission flight envelope. This requires advanced controllers that have sufficient robustness, track complex trajectories, and use all the vehicles control capabilities at higher levels of accuracy. In this work, a robust nonlinear model predictive controller is designed to command and control an unmanned aerial system to track complex tight trajectories in the presence of internal and external perturbance. The Flight System developed in this work achieves the above performance by using: 1 A nonlinear guidance algorithm that enables the vehicle to follow an arbitrary trajectory shaped by moving points; 2 A formulation that embeds the guidance logic and trajectory information in the aircraft model, avoiding cross coupling and control degradation; 3 An artificial neural network, designed to adaptively estimate and provide aerodynamic and propulsive forces in real-time; and 4 A mixed sensitivity approach that enhances the robustness for a nonlinear model predictive controller overcoming the effect of un-modeled dynamics, external disturbances such as wind, and measurement additive perturbations, such as noise and biases. These elements have been integrated and tested in simulation and with previously stored flight test data and shown to be feasible

    Dynamics and Control of Spacecraft Rendezvous By Nonlinear Model Predictive Control

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    This doctoral research investigates the fundamental problems in the dynamics and control of spacecraft rendezvous with a non-cooperative tumbling target. New control schemes based on nonlinear model predictive control method have been developed and validated experimentally by ground-based air-bearing satellite simulators. It is focused on the autonomous rendezvous for a chaser spacecraft to approach the target in the final rendezvous stage. Two challenges have been identified and investigated in this stage: the mathematical modeling of the targets tumbling motion and the constrained control scheme that is solvable in an on-line manner. First, the mathematical description of the tumbling motion of the target spacecraft is proposed for the chaser spacecraft to rendezvous with the target. In the meantime, the practical constraints are formulated to ensure the safety and avoid collision during the final approaching stage. This set of constraints are integrated into the trajectory planning problem as a constrained optimization problem. Second, the nonlinear model predictive control is proposed to generate the feedback control commands by iteratively solving an open-loop discrete-time nonlinear optimal control problem at each sampling instant. The proposed control scheme is validated both theoretically and experimentally by a custom-built spacecraft simulator floating on a high-accuracy granite table. Computer software for electronic hardware for the spacecraft simulator and for the controller is designed and developed in house. The experimental results demonstrate the effectiveness and advantages of the proposed nonlinear model predictive control scheme in a hardware-in-the-loop environment. Furthermore, a preliminary outlook is given for future extension of the spacecraft simulator with consideration of the robotic arms

    Price-based control for electrical power distribution system

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    On Approximation of Linear Network Systems

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