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Effective Optimization for Fuzzy Model Predictive Control
 IEEE Transactions on Fuzzy Systems
, 2004
"... Abstract—This paper addresses the optimization in fuzzy model predictive control. When the prediction model is a nonlinear fuzzy model, nonconvex, timeconsuming optimization is necessary, with no guarantee of finding an optimal solution. A possible way around this problem is to linearize the fuzzy ..."
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Abstract—This paper addresses the optimization in fuzzy model predictive control. When the prediction model is a nonlinear fuzzy model, nonconvex, timeconsuming optimization is necessary, with no guarantee of finding an optimal solution. A possible way around this problem is to linearize the fuzzy model at the current operating point and use linear predictive control (i.e., quadratic programming). For longrange predictive control, however, the influence of the linearization error may significantly deteriorate the performance. In our approach, this is remedied by linearizing the fuzzy model along the predicted input and output trajectories. One can further improve the model prediction by iteratively applying the optimized control sequence to the fuzzy model and linearizing along the so obtained simulated trajectories. Four different methods for the construction of the optimization problem are proposed, making difference between the cases when a single linear model or a set of linear models are used. By choosing an appropriate method, the user can achieve a desired tradeoff between the control performance and the computational load. The proposed techniques have been tested and evaluated using two simulated industrial benchmarks: pH control in a continuous stirred tank reactor and a highpurity distillation column. Index Terms—Linearization, model predictive control, multipleinput–multipleoutput systems (MIMO), nonlinear control, quadratic programming, Takagi–Sugeno fuzzy models. I.
Policies for simultaneous estimation and optimization
 in American Control Conference
, 1999
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Recurrent neural networks for solving secondorder cone programs
"... a b s t r a c t This paper proposes using the neural networks to efficiently solve the secondorder cone programs (SOCP). To establish the neural networks, the SOCP is first reformulated as a secondorder cone complementarity problem (SOCCP) with the KarushKuhnTucker conditions of the SOCP. The S ..."
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a b s t r a c t This paper proposes using the neural networks to efficiently solve the secondorder cone programs (SOCP). To establish the neural networks, the SOCP is first reformulated as a secondorder cone complementarity problem (SOCCP) with the KarushKuhnTucker conditions of the SOCP. The SOCCP functions, which transform the SOCCP into a set of nonlinear equations, are then utilized to design the neural networks. We propose two kinds of neural networks with the different SOCCP functions. The first neural network uses the FischerBurmeister function to achieve an unconstrained minimization with a merit function. We show that the merit function is a Lyapunov function and this neural network is asymptotically stable. The second neural network utilizes the natural residual function with the cone projection function to achieve low computation complexity. It is shown to be Lyapunov stable and converges globally to an optimal solution under some condition. The SOCP simulation results demonstrate the effectiveness of the proposed neural networks.
Multiobjective Control: Linear Matrix Inequality Techniques and Genetic Algorithms Approach
, 2005
"... In accordance with the copyright legislation no information derived from the dissertation nor quotation from it may be published without full acknowledgment of the source being made nor any substantial extract from the dissertation published without the author’s written consent. This thesis addresse ..."
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In accordance with the copyright legislation no information derived from the dissertation nor quotation from it may be published without full acknowledgment of the source being made nor any substantial extract from the dissertation published without the author’s written consent. This thesis addresses some of the open problems in multiobjective control. The aim of this thesis is to compare two emerging techniques in multiobjective control: evolutionary algorithms (EAs) and convex optimisation over linear matrix inequalities (LMIs). In the multiobjective control problem, a tradeoff is sought between competing objectives. In such a problem, no single optimal solution exists, rather a set of equally valid solutions, known as the Pareto optimal set. It has been shown that the multiobjective control problem can be tackled with LMI techniques, due to its ability to include convex constraints such as H2 performance, H ∞ performance, and poleplacement. The multiobjective control problem is formulated as a semidefinite
ROBUST LINEAR PROGRAMMING AND OPTIMAL CONTROL
"... Abstract: The paper describes an ef£cient method for solving an optimal control problem that arises in robust modelpredictive control. The problem is to design the input sequence that minimizes the peak tracking error between the ouput of a linear dynamical system and a desired target output, subje ..."
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Abstract: The paper describes an ef£cient method for solving an optimal control problem that arises in robust modelpredictive control. The problem is to design the input sequence that minimizes the peak tracking error between the ouput of a linear dynamical system and a desired target output, subject to inequality constraints on the inputs. The system is uncertain, with an impulse response that can take arbitrary values in a given polyhedral set. This problem can be formulated as a robust linear programming problem with structured uncertainty. The presented method is based on Mehrotra’s interiorpoint method for linear programming, and takes advantage of the problem structure to achieve a complexity that grows linearly with the control horizon, and increases as a cubic polynomial as a function of the system order, the number of inputs, and the number of uncertainty parameters. Keywords: Linear programming. Convex optimization. Modelpredictive control. 1.