In this paper, we consider an interesting identification problem where an unknown phenomenon is to be identified by the trajectory of an impulsive differential equation. The system coefficients, the locations of the s...
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In this paper, we consider an interesting identification problem where an unknown phenomenon is to be identified by the trajectory of an impulsive differential equation. The system coefficients, the locations of the switching time points, and the heights of the jumps at these time points are to be determined such that the summation of the least square errors of the trajectory of the impulsive system and the phenomenon over the observed time points is minimized. This becomes an interesting dynamical optimization problem. We develop an efficient computational method for solving this dynamical optimization problem. Our approach first is to use the control parameterization enhancing transform to convert this dynamical optimization problem into an equivalent optimal parameter selection problem, where the varying time points are being mapped into fixed time points. Then, the gradient formula of the cost function is derived. Thus, this optimal parameter selection problem can be solved as a mathematical programming problem. For illustration, a numerical example is solved by using the proposed method. (c) 2005 Elsevier Ltd. All rights reserved.
In this paper, we consider a class of optimal parameter selection problems with continuous inequality constraints. By introducing a smoothing parameter, we formulate a sequence of KKT (Karush-Kuhn-Tucker) systems of t...
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In this paper, we consider a class of optimal parameter selection problems with continuous inequality constraints. By introducing a smoothing parameter, we formulate a sequence of KKT (Karush-Kuhn-Tucker) systems of this problem and then transform it into a system of constrained nonlinear equations. Then, the first- and second-order gradients formulae of the cost functional and the constraints are derived. On this basis, a smoothing projected Newton-type algorithm is developed to solving this system of nonlinear equations. To illustrate the effectiveness of the proposed method, some numerical results are solved and presented.
In this paper, we consider a class of optimal control problems in which the dynamical system involves a finite number of switching times together with a state jump at each of these switching times. The locations of th...
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In this paper, we consider a class of optimal control problems in which the dynamical system involves a finite number of switching times together with a state jump at each of these switching times. The locations of these switching times and a parameter vector representing the state jumps are taken as decision variables. We show that this class of optimal control problems is equivalent to a special class of optimal parameter selection problems. Gradient formulas for the cost functional and the constraint functional are derived. On this basis, a computational algorithm is proposed. For illustration, a numerical example is included.
This paper considers an optimal control problem of nonlinear Markov jump systems with continuous state inequality constraints. Due to the presence of continuous-time Markov chain, no existing computation method is ava...
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This paper considers an optimal control problem of nonlinear Markov jump systems with continuous state inequality constraints. Due to the presence of continuous-time Markov chain, no existing computation method is available to solve such an optimal control problem. In this paper, a derandomisation technique is introduced to transform the nonlinear Markov jump system into a deterministic system, which simultaneously gives rise to an equivalent deterministic dynamic optimisation problem. The control parametrisation technique is then used to partition the time horizon into a sequence of subintervals such that the control function is approximated by a piecewise constant function consistent with the partition. The heights of the piecewise constant function on the corresponding subintervals are taken as decision variables to be optimised. In this way, the approximate dynamic optimisation problem is an optimal parameter selection problem, which can be viewed as a finite dimensional optimisation problem. To solve it using a gradient-based optimisation method, the gradient formulas of the cost function and the constraint functions are derived. Finally, a real-world practical problem involving a bioreactor tank model is solved using the method proposed.
In this paper, an optimal PID-like controller is proposed for a spacecraft attitude stabilization problem subject to continuous inequality constraints on the spacecraft angular velocity and control, as well as termina...
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In this paper, an optimal PID-like controller is proposed for a spacecraft attitude stabilization problem subject to continuous inequality constraints on the spacecraft angular velocity and control, as well as terminal constraints on the spacecraft attitude and angular velocity. The closed-loop stability is established using the Lyapunov stability theory. The constraint transcription method and a local smoothing technique are used to construct a smooth approximate function for each of the continuous inequality constraints on the angular velocity and control. Then, by using the concept of the penalty function, these approximate smooth functions are appended to the quadratic performance criterion forming an augmented cost function. Consequently, the constrained optimal control problem under the PID-like controller is approximated by a sequence of optimal parameter selection problems subject to only terminal constraints on the spacecraft attitudes. A reliable computational algorithm is derived for the tuning of the optimal PID-like control parameters. Finally, numerical simulations are carried out to illustrate the effectiveness of the methodology proposed. (C) 2011 Elsevier Ltd. All rights reserved.
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