Mathematical models of a three-wheeled mobile robot based on the variable state apparatus and in the operator’s form are presented. Based on these mathematical models, the synthesis of its adaptive control system is carried out according to the method of constructing Ziegler-Nichols PID controllers, as well as modal PID controllers. The design method of proportional controllers with double differentiation (PDD) of the autonomous robot is justified. The rules of wheel pair control are synthesized on the basis of reference models using a simple gradient scheme of the inverse problems method of dynamics in the formulation of P. D. Krutko for the problem of stabilizing (blanking) the angular velocities for a three-wheeled mobile robot. Simulink-models of robot movement are developed for cases with the use of PID-controllers which are adjusted by the Ziegler-Nichols method at synchronous deviation of wheels. Simulink-models of robot motion have been developed for cases using PID controllers set up according to the Ziegler-Nichols method for synchronous wheel deflection, modal and real PID controllers for differential wheel deflection, as well as double differentiation controllers. The analysis of modeling results is considered.

Analytical design of optimal controllers for nonlinear systems is studied. To refine the method related to minimization of the general work functional, the initial control problem is transformed to a degenerate problem and solved with a suitable strategy. The joint control design strategy is the construction of minimizing sequences, which converge in intervals by stationarity to the optimal process of the initial problem. An illustrative example is given.

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