Titlebook: Optimization and Control of Dynamic Systems; Foundations, Main De Henryk Górecki Book 2018 Springer International Publishing AG 2018 Vector

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Linear Quadratic Problems [1],and effective and efficient control algorithms which at first found application in the military and space control and then have been employed for to process control, power systems, biological systems and economy, to just name a few.

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Some Fundamental Mathematical Models,For the description of the evolution of a process in time it is assumed, in the simplest case, that the future state of the process .(.) for . depends only on the state . at . and the control ., and the rate of change of the process is the time derivative of the state vector.

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Fundamental Properties and Requirements of Control Systems,One of the fundamental properties that is required of a control system is that the state and output response to a bounded control input acting in the time interval . be also bounded. This property is called the .. Yet there is another definition of stability which is more often used. Namely, it is the stability in the Lyapunov sense.

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Extrema Subject to Equality Constraints,The previous chapter dealt with the necessary and sufficient conditions for the existence of extrema of functions in the interiors of their domains without any additional constrains.

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Parametric Optimization of Continuous Linear Dynamic Systems,Parametric optimization includes a range of problems in which the mathematical model of a considered system is in principle determined, and what remains to be done is to determine the optimum values of certain free parameters which are used in the equations which describe the system.

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Dynamic Programming [1, 2, 4, 5],Consider again the problem of optimal control of a process described by the following differential equation ..