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A constructive method for solving the linear-quadratic problem of the optimal control of a parabolic-type system with distributed parameters is proposed under the condition of the uniform estimation of the target sets. The optimality criterion takes the form of an integral quadratic estimate of the controlled state function in the spatiotemporal domain of its definition. A parameterized representation of the control inputs is given with the required accuracy within special intervals of the optimal process, where the control inputs cannot be determined using first-order analytical optimality conditions. The proposed approach is based on the previously developed alternance method for constructing parameterized algorithms of programmed control, which heavily relies on the fundamental regularities of the subject area. It is demonstrated that the equations of the optimal regulators within the special intervals are reduced to the linear feedback algorithms based on the measured states of the objects. These algorithms are supplemented with switches at the boundary points to apply the admissible control inputs corresponding to the calculated values of the controlled variable. [ABSTRACT FROM AUTHOR]

A constructive method is proposed for solving a linear-quadratic problem of the robust optimization of spatiotemporal control actions in systems with distributed parabolic parameters under conditions of interval uncertainty of the time-invariant parametric characteristics of an object. In accordance with the control strategy according to the principle of the best guaranteed result, the assessment of achievable target sets of the controlled system is carried out according to the accuracy of uniform approximation to the required final state on an extended set of arguments, which includes, in addition to spatial variables, the entire admissible set of uncertain factors. The developed approach is based on the previously developed alternance method for constructing parameterizable program control algorithms, which extends the results of the theory of nonlinear Chebyshev approximations to a wide range of optimization problems and uses the fundamental laws of the subject area. It is shown that the proposed equations of optimal controllers, which are reduced to linear feedback laws on the measured state of the object with nonstationary transmission coefficients, lead to achievable values of the optimality criteria that do not exceed their upper bounds under the considered uncertainty conditions. [ABSTRACT FROM AUTHOR]

A constructive method is proposed for solving a linear-quadratic spatiotemporal control problem in systems with distributed parabolic parameters under the conditions of the given accuracy of uniform approximation of the final state of a plant to the required spatial distribution of the controlled variable. The developed approach is based on the previously developed alternance method for constructing parameterizable programmed control algorithms, which extends the results of the theory of nonlinear Chebyshev approximations to a wide range of optimization problems and uses the fundamental laws of the subject area. It is shown that the equations of optimal controllers with autonomous modal controls in the open domain of their definition and taking into account restrictions on the nature of the spatial distribution of the control actions specified by the conditions of technical implementation are reduced to linear feedback algorithms for the measured state of the plant with nonstationary transmission coefficients and the given dependence on the spatial arguments of the controlled value. The results obtained are extended to the problem of searching for time-invariant spatially distributed controls, considered as the desired design solutions for a plant. [ABSTRACT FROM AUTHOR]

A constructive method for synthesizing the optimal control of deterministic and not completely determined systems with distributed parabolic parameters under the conditions of the prescribed accuracy of a uniform approximation of the terminal plant state to the required spatial distribution of the controlled variable is proposed. This approach is based on the earlier developed alternance method for constructing optimal open-loop control algorithms, which extends the results of the theory of nonlinear Chebyshev approximations to a wide range of parameterizable optimal control problems and takes into account fundamental features of the domain. It is shown that the optimal controller equations are reduced to linear output feedback equations with time-dependent coefficients that are calculated based on incomplete measurements of the system's state with an error that decreases as the number of modal components of the controlled variable that are taken into account increases. [ABSTRACT FROM AUTHOR]

A constructive solution of the optimal energy-efficient programmed control problem for distributed parameter systems with a given-precision uniform approximation of the space distribution of the controlled variable with respect to the desired state is proposed. The computational algorithm developed below involves a special-form preliminary parametrization procedure for control actions on finite-dimensional subsets of the terminal values of conjugate variables in the boundary-value problem of Pontryagin's maximum principle, in combination with the subsequent reduction to a semi-infinite optimization problem, which is solved with respect to the requisite parameter vector using the alternance method suggested earlier. An example of optimal energy-efficient control of transient heat conduction, which is of independent interest, is given. [ABSTRACT FROM AUTHOR]

We propose a constructive technology for solving parametrizable problems of multichannel optimal control in systems with distributed parameters under conditions of a given accuracy of uniform approximating the resultant spatial distribution of the controlled variable to the desired state. The developed technique uses the parametrization procedure of the sought control actions and the subsequent reduction to the special form of the task of semi-infinite optimization, which is solved by the scheme of the alternance method proposed earlier; this scheme is generalized to the investigated situation. We present an example (which is of interest by itself) of time-optimization of the process of nonstationary heat conductivity with two boundary control actions. [ABSTRACT FROM AUTHOR]

A constructive technology of the solution of the parametrized problems of the programmed optimal control of systems with the distributed parameters under the conditions of different requirements for the permissible deviation of the resulting spatial distribution of the controlled value from the set magnitude in the uniform metric is proposed. The developed technique uses a special procedure of the one-criterion convolution of the considered constraints and the subsequent reduction to the typical form of the problems of mathematical programming on the extremum of a function of a finite number of variables with an infinite number of constraints (semi-infinite optimization problem), which is solved by the scheme of the previously developed alternance method. An example of optimization by the criteria of the speed and energy consumption of unsteady heat conduction processes with two different restrictions on the accuracy of approximation to the given temperature conditions, which is of independent interest, is given. [ABSTRACT FROM AUTHOR]

The previously developed methods for analyzing the controllability of linear multidimensional plants with distributed parameters on a given set of open-loop trajectories of their transfer into the desired finite state are extended to interconnected physically heterogeneous distributed dynamic systems. An example (which is of independent interest) of estimating the open-loop controllability of nonstationary heat conduction processes under the conditions of the perfect contact of the interacting environments is presented. [ABSTRACT FROM AUTHOR]

A constructive method for the design and real-time implementation of parameterized open-loop controls in the optimal feedback control of ensembles of trajectories of incompletely determined parabolic systems with distributed parameters is proposed. This method uses reduction to semiinfinite optimization problems, alternance properties of their solutions, and additional information about fundamental laws of the application domain. The practical application of the results is illustrated by the example of controlling nonstationary temperature fields under multiple disturbances, which is a problem of independent interest. [ABSTRACT FROM AUTHOR]

The problem of controllability of linear multidimensional models of dynamical systems with distributed parameters is considered for a given set of open-loop trajectories that transfer the plant into the terminal state. Based on the behavior of these trajectories in the spatial and temporal domain, we obtain necessary and sufficient conditions (that can be directly checked) for the existence of various technologically feasible controls ensuring that the necessary requirements are met. Using the methods proposed in this study, we give examples (which are of independent interest) for estimating the open-loop controllability of nonstationary heat conduction processes. [ABSTRACT FROM AUTHOR]

The minimization problem for deviations of the stationary state of a system with distributed parameters from a desired state estimated in the uniform metric is considered. A constructive method for its solution using a successive parameterization of controls and the alternance properties of optimal spatial distributions of the controlled variable is proposed. Examples of the use of the proposed computational scheme of the organization of computational algorithms in optimization problems of stationary thermal conductivity processes are discussed. [ABSTRACT FROM AUTHOR]

The problem of analytical construction of aggregated automatic controllers for various types of control actions in systems with distributed parameters described by parabolic partial differential equations is considered. Synthesis algorithms based on the proposed forms of aggregated macro-variables are studied. A boundary control system for the process of non-stationary thermal conductivity is constructed to illustrate the results. [ABSTRACT FROM AUTHOR]

A special procedure for control action parameterization and the precise method based on it for determining open-loop optimal control algorithms for the systems with distributed parameters under the prescribed tolerance conditions for the deviation from the required final state of the controlled parameter being estimated in the uniform metric is proposed. The method uses the reduction to the problems of semi-infinite optimization, alternance properties of their solutions, and some additional information on fundamental regularities of the subject domain. Examples showing an opportunity of using these results for applied problems, constituting also a point of independent interest are presented. [ABSTRACT FROM AUTHOR]

The problem of synthesizing automatic controllers for one class of linear plants with distributed parameters is considered from the general point of structural theory of distributed systems. On this basis, methods to construct control algorithms for various modifications of control actions are proposed. The results obtained are illustrated by examples of synthesizing automatic control systems of nonstationary heat conduction processes. [ABSTRACT FROM AUTHOR]