This paper provides a design method of fixed-structure robust controllers satisfying multiple H ∞ norm specifications by using a sort of randomized algorithms. First, a new tool to perform general constrained optimiz...
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This paper provides a design method of fixed-structure robust controllers satisfying multiple H ∞ norm specifications by using a sort of randomized algorithms. First, a new tool to perform general constrained optimization is developed which does not need any gradient or derivative of the objective function. This tool is based on PSO (particle swarm optimization), which attracts a lot of attention recently in the evolutionary computation area due to its empirical evidence of its superiority in solving various non-convex problems. Second, it is shown how to design a fixed-structure controller satisfying given multiple H ∞ specifications by using the developed optimization tool. Third, its effectiveness is evaluated through various numerical examples, because it is difficult to guarantee the performance of the proposed method theoretically due to a probabilistic nature of the PSO. The simulation results demonstrate its effectiveness clearly.
This paper deals with problems of impulse control which allow control inputs consisting not only of delta functions but also of their higher derivatives (impulses of higher order). The controls are sought for in the f...
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This paper deals with problems of impulse control which allow control inputs consisting not only of delta functions but also of their higher derivatives (impulses of higher order). The controls are sought for in the form of feedback strategies which leads to the application of respective generalized dynamic programming techniques, where the role of traditional Hamilton–Jacobi–Bellman equations is taken by respective variational inequalities of similar structure. Further proposed are physically realizable approximations which converge to these ideal solutions. Since the ideal solutions allow to transfer a controllable system from one given position to another in zero time, their approximations lead us to physically realizable “fast” controls with piecewise constant realizations. Such feedback control inputs are then compared with traditional bang-bang type strategies and turn out to be more robust. Computational schemes for related problems of reachability and control synthesis are further described with examples of damping oscillating systems of high order in minimal time being demonstrated.
This paper deals with fixed-order controller design problems with output-feedback. It is well known that the control problems are difficult to be solved, because they become non-convex problems described by bilinear m...
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This paper deals with fixed-order controller design problems with output-feedback. It is well known that the control problems are difficult to be solved, because they become non-convex problems described by bilinear matrix inequality(BMI). In this paper, a new exterior-point approach to such BMI problems is proposed. This approach produces a controller sequence from a infeasible region to a feasible one. The advantage of this approach is that non-stabilizing controllers can be used as an initial controller. Numerical examples show the efficiency of our method.
This paper is concerned with the mixed H 2 /H ∞ control problem via static output feedback control. The main purpose of this paper is to give an iterative method for finding a sub-optimal static output-feedback contr...
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This paper is concerned with the mixed H 2 /H ∞ control problem via static output feedback control. The main purpose of this paper is to give an iterative method for finding a sub-optimal static output-feedback controller for the mixed H 2 /H ∞ control problem. The contribution of this paper is to derive a gradient of the H 2 cost function. Using this gradient, we propose a gradient method for H 2 and mixed H 2 /H ∞ control problems. Numerical examples show the efficiency of our methods.
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