parameter estimation in nonlinear distributed-parameter systems is usually accomplished by minimizing an output least-square criterion, which is defined implicitly through the solution of the model equations. This pap...
详细信息
parameter estimation in nonlinear distributed-parameter systems is usually accomplished by minimizing an output least-square criterion, which is defined implicitly through the solution of the model equations. This paper addresses itself to two important practical issues of the parameter-estimation procedure, i.e., the numerical procedure used to compute the gradient of the criterion with respect to the unknown parameters, and the selection of experimental conditions, i.e., sensor locations and input signals. An experiment design procedure based on the sensitivity matrix is presented. The methods for gradient computation and experiment design have been successfully applied to several process models, and are illustrated in this paper with a simple heat-conduction problem and a more complex model of a catalytic fixed-bed reactor.
A distributed-parameter model of a continuous-flow fixed-bed reactor is studied. The main emphasis lies on a structural property of the partial differential equation (PDE) system model. This property, which in lumped ...
详细信息
A distributed-parameter model of a continuous-flow fixed-bed reactor is studied. The main emphasis lies on a structural property of the partial differential equation (PDE) system model. This property, which in lumped parametersystems is called the nonminimum phase property, has certain implications in the controller design. The controller design for the PDE model is constructed via semidiscretisation. The only space variable of the PDE model is discretised by using Galerkin's finite element method (FEM). For some parameter values of the PDE model the linearising control of the semidiscretised model results in unstable behaviour in the sense that the zero dynamics of the model is unstable. This same unstable behaviour was also earlier observed in using the orthogonal collocation for the semidiscretisation. Connections between the location of the zeros of the original PDE model linearised around its steady-state solution and the stability/instability properties of the linearising control of the semidiscrete model are discussed in relation to the same issues in lumped-parameter differential system models.
We consider the problems of identifying the parameters a(ij)(x), b(i)(x), c(x) in a 2nd order, linear, uniformly elliptic equation, [GRAPHICS] on the basis of measurement data [GRAPHICS] with an equality constraint an...
详细信息
We consider the problems of identifying the parameters a(ij)(x), b(i)(x), c(x) in a 2nd order, linear, uniformly elliptic equation, [GRAPHICS] on the basis of measurement data [GRAPHICS] with an equality constraint and inequality constraints on the parameters. The cost functionals are one-sided Gateaux differentiable with respect to the state variables and the parameters. Using the Duboviskii-Milyutin lemma, we get maximum principles for the identification problems, which are necessary conditions for the existence of optimal parameters.
The problem of optimizing the efficiency of a fixed-bed bioreactor by manipulating the feed flowrate and the inlet concentration is addressed. A simple macroscopic model of the bio-filter is developed for this purpose...
详细信息
The problem of optimizing the efficiency of a fixed-bed bioreactor by manipulating the feed flowrate and the inlet concentration is addressed. A simple macroscopic model of the bio-filter is developed for this purpose. Two criteria, one maximizing the space efficiency and the other the time efficiency of wastewater treatment, are proposed. It is shown that, optimal operation is obtained when one of the input variables is set to its upper limit and the other adjusted such that the effluent quality is met. The optimal input is calculated using a feedback structure which also helps tackle large perturbations inherent to biological systems. Finally, an improved operational scheme, termed the pseudo-batch mode , is developed for which both the time and the space criteria are maximized simultaneously.
The paper presents recent results by the authors on minimax control design of parabolic systems in uncertainty conditions under hard control and state constraints. The design procedure involves multi-step approximatio...
详细信息
The paper presents recent results by the authors on minimax control design of parabolic systems in uncertainty conditions under hard control and state constraints. The design procedure involves multi-step approximations and takes into account monotonicity properties of the parabolic dynamics. The results obtained justify a suboptimal three-positional structure of feedback controllers in the Dirichlet and Neumann boundary conditions and provide calculations of their optimal parameters that ensure the required state performance and stability under any admissible perturbations.
In this paper, we present our recent results which may play a role in improving the situation in the practical implications of mathematical modeling of cancer chemotherapy. We are concerned with control problems for a...
详细信息
In this paper, we present our recent results which may play a role in improving the situation in the practical implications of mathematical modeling of cancer chemotherapy. We are concerned with control problems for a model of the dynamics of emergence of resistance of cancer cells to chemotherapy, as understood based on recent progress in molecular biology. In some special cases of this model, their asymptotic behavior and the stability problem for the infinite dimensional case were studied. In the case of finite initial condition the stability conditions were derived by asymptotical analysis of the analytical solution to the system of equations. In the case of initial condition with infinite number of elements the stability verification was based on the spectral properties of the infinitesimal generator of the system.
Two types of algoritms of optimization of controlled processes described by semi-linear hyperbolic equations systems are suggested in this paper. The first type of algorithms is based on the analogue of L.S. Pontryagi...
详细信息
Two types of algoritms of optimization of controlled processes described by semi-linear hyperbolic equations systems are suggested in this paper. The first type of algorithms is based on the analogue of L.S. Pontryagin's needle variation and its convergence is realized in the sense of tendency to the maximum principle. The second type of algorithms is constructed basing on the analogue of inner variation. This algorithm is considered for hyperbolic systems with additional integral constraints. Neither techniques of Lagrange multipliers nor ideas of penalty functions are used, although they are usually applied to solve optimization problems with additional constraints. The algorithm converges to new necessary conditions of optimality.
A maximum principle is developed for a class of problems involving the optimal control of a damped-parameter system governed by a linear hyperbolic equation in one space dimension that is not necessarily separable. A ...
详细信息
A maximum principle is developed for a class of problems involving the optimal control of a damped-parameter system governed by a linear hyperbolic equation in one space dimension that is not necessarily separable. A convex index of performance is formulated, which consists of functionals of the state variable, its first- and second-order space derivatives, its first-order time derivative, and a penalty functional involving the open-loop control force. The solution of the optimal control problem is shown to be unique. The adjoint operator is determined, and a maximum principle relating the control function to the adjoint variable is stated. The proof of the maximum principle is given with the help of convexity arguments. The maximum principle can be used to compute the optimal control function and is particularly suitable for problems involving the active control of structural elements for vibration suppression.
A dynamic system with distributedparameters the spatial motion of which is described by partial differential equations is considered. The system is affected by external control forces concentrated at specified points...
详细信息
A dynamic system with distributedparameters the spatial motion of which is described by partial differential equations is considered. The system is affected by external control forces concentrated at specified points. Quadratic integral constraints are imposed on the actions. The problem of minimizing the integral quadratic functional of the state of the system by selecting the forces to be functions of time and of their points of application is posed. Optimization of the points of application of the forces is discussed. An example is presented.
暂无评论