Optimal control is whereby the requirements are formulated as either the minimization of a cost index or the maximization of a performance index of an operational control system.
Optimal control is utilized in a number of disciplines such as aircraft and spacecraft, satellites and aerospace, communications engineering, robots and robotics, electric drives, power systems, computer and computer systems, chemical engineering and so forth.
If a process is operating under a steady-state condition, optimization considers the process stationary, and is concerned only with the operating points. When the process is stationary, the resulting optimum operating point can easily be maintained by setting the preset set points and pre-calculated control parameters. However, if the process changes from time to time, new optimum set points for the system need to be established for each stage.
The performance of a system is usually optimized for several reasons, such as improving the quality, increasing the production, decreasing waste, achieving greater efficiency, maximizing the safety, saving time and energy, and so forth. In many optimization problems, the boundary conditions are imposed by the system for safety in operations, availability of minimum and maximum power, limitations in storage capacity, capability of the operating machinery, temperature, speed, acceleration, force, etc.
Optimal control problems may be solved in a number of ways depending on the nature of the problem. For instance, if the performance index and constraints can be formulated as linear algebraic functions of the controlled variables, then selection of the linear programming may be the best way to go. Simplex techniques may offer a good way of solving the linear programming problem. On the other hand, if the equations describing the system are nonlinear, then the solution may involve nonlinear techniques or linearization of the problem in some regions. For problems involving the determination of the largest of a function with two or more variables, then the steepest ascent or descent/gradient technique may be suffice.
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