We consider the problems for identifying the parameters a(11)(x, t),...,a(mm)(x, t) and c(x, t) involved in a second-order, linear, uniformly parabolic equation partial derivative(t)u - partial derivative(i)(a(ij) (x,...
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We consider the problems for identifying the parameters a(11)(x, t),...,a(mm)(x, t) and c(x, t) involved in a second-order, linear, uniformly parabolic equation partial derivative(t)u - partial derivative(i)(a(ij) (x, t)partial derivative(j)u) + bi(x, t)partial derivative(i)u + c(x, t)u = f(x, t) in Omega x (0, T), u\(partial derivative Omega) = g, u\(t = 0) = u(0)(x), x is an element of Omega. on the basis of noisy measurement data z(x) = u(x, T) + w(x), x is an element of Omega with equality and inequality constraints on the parameters and the state variable. The cost functionals are (one-sided) Gateaux-differentiable with respect to the state variables and the parameters. Using the Duboviskii-Miljutin lemma we get the two maximum principles for the two identification problems, respectively, i.e., the necessary conditions for the existence of optimal parameters.
This letter presents an event-driven observer-based control strategy for a class of delayed distributed parameter systems (DPSs) by using the mobile actuator-plus-sensor (APS) network. By designing the trajectories of...
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This letter presents an event-driven observer-based control strategy for a class of delayed distributed parameter systems (DPSs) by using the mobile actuator-plus-sensor (APS) network. By designing the trajectories of the mobile devices, the control performance is improved due to the increasing utilization efficiency of the devices. In addition, to mitigate the unnecessary waste of the communication resources, an event-driven observer-based controller is proposed. Then, using the designed operators, the delayed DPS is transformed into an evolution equation in a Hilbert space. Besides, based on the Lyapunov stability theory, the solution to the delayed distributedparameter system under the designed strategy is proven to be globally uniformly ultimately bounded. Finally, a numerical example is provided to verify the feasibility and effectiveness of the proposed method.
A discrete-time adaptive filter is derived for a distributed system described by a linear partial differential equation with some unknown random constants whose a priori probabilities are known. The system concerned c...
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A discrete-time adaptive filter is derived for a distributed system described by a linear partial differential equation with some unknown random constants whose a priori probabilities are known. The system concerned contains the Gaussian white noise in time, and its measurement system is treated as a so-called pointwise observation in which the measurement is taken at the finite discrete subdomains in the coordinate spaces. The use is conceptually made of an adaptive technique based on the Bayesian method and it is shown that the optimal distributed filter proposed here can be partitioned into two parts, a linear nonadaptive part that consists of a bank of distributed Kalman-Bucy type filters and a nonlinear part that incorporates the learning nature of the estimator. For the derivation of each “elemental filter”, the discrete-time innovation theory is utilized. The eigenfunction expanding method in a complete orthonormal system is applied for the numerical procedure of the proposed filter. From the simulation of the estimation problem for the neutron flux distribution in a slab type nuclear reactor, the proposed adaptive filter is shown to have attractive characteristics and therefore can be recommended for practical online adaptive estimation of distributed parameter systems.
System parameter values can vary from their assumed nominal values. These perturbations may alter the performance of a distributedparameter system from the desired nominal performance to an unacceptable degree. To ov...
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System parameter values can vary from their assumed nominal values. These perturbations may alter the performance of a distributedparameter system from the desired nominal performance to an unacceptable degree. To overcome these undesirable effects it may be possible to utilize feedback control in the system to insure that parameter variations alter the system performance with feedback to a lesser degree than an equivalent open-loop system subject to the same perturbations. New results are developed in the form of sufficient conditions to insure that feedback compensation decreases the effects of parameter variations upon the system dynamics for distributed parameter systems described by linear constant-coefficient partial differential equations which may be nonseparable. The theory is applied to two examples, the most significant of which is that of heat exchange between a moving and a stationary medium such as heating material in a through-passage furnace.
In the paper we present certain results on the question of controllability for (i) linear evolution equations (parabolic and hyperbolic) with distributed controls and (ii) a class of linear parabolic equations with bo...
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In the paper we present certain results on the question of controllability for (i) linear evolution equations (parabolic and hyperbolic) with distributed controls and (ii) a class of linear parabolic equations with boundary controls.
The problem of identifying Green's function of a linear time-invariant distributedparameter system is considered. A discrete lumped version of the distributed system is developed for which a pointwise approximati...
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The problem of identifying Green's function of a linear time-invariant distributedparameter system is considered. A discrete lumped version of the distributed system is developed for which a pointwise approximation of Green's function is the state transition matrix. A stochastic approximation algorithm is presented for the identification of the pointwise approximation of Green's function in the presence of additive measurement noise.
A design method of adaptive H∞ consensus control of multi-agent systems composed of a class of infinite-dimensional systems on directed network graphs, is presented in this paper. The proposed control scheme is deriv...
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Most of the controller design in distributed parameter systems requires not only the measurement and/or estimation of distributed states, but also the feedback gain in a function of time and spatial coordinates. These...
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Most of the controller design in distributed parameter systems requires not only the measurement and/or estimation of distributed states, but also the feedback gain in a function of time and spatial coordinates. These requirements are difficult, if nor impossible, to meet in engineering implementation An output feedback algorithm for the structural control of distributed parameter systems is presented in this paper. The algorithm employs a solution technique to simplify the functional Riccati equation into a set of algebraic equations such that sensor nod actuator can be applied at discrete, instead of distributed, locations in the structure systems. The control law does nor require any model discretization thereby preventing the spillover associated,vith discrete parameter models. An example of a slewing beam system distributedparameter model is employed to demonstrate that the bending vibration can be effectively suppressed by a control input at the hub together with a minimal set of output measurements. The performance of the controller is shown superior to that of discrete systems using modal truncation techniques.
The control of distributed parameter systems with constant, but unknown parameters is considered. A weighted average of the distributed output on the spatial domain is defined as a new variable and is used to generate...
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The control of distributed parameter systems with constant, but unknown parameters is considered. A weighted average of the distributed output on the spatial domain is defined as a new variable and is used to generate the control. The parameters of the model are estimated using recursive least squares estimation. The control is obtained using a minimum variance strategy based on the estimated parameters. distributed disturbances and measurement noise are allowed to be present. Measurements at a finite number of points in the spatial domain are used in obtaining a discrete-time model. From the simulation of a one-sided heating diffusion process the self-tuning regulator is shown to have attractive characteristics and hence can be recommended for practical on-line control of distributed parameter systems.
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