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This paper studies the problem of designing an incentive strategy for a leader–follower dynamic game affected by some sort of uncertainties. As is traditionally understood in the standard theory of incentives, the leader has complete knowledge of the game parameters, including the follower's performance index. So then he can compute the strategy that will lead the game to the global optimum that is favourable for him. Most of the current work is devoted to this situation. Nevertheless, such an assumption is unrealistic. This paper proposes an incentive scheme in which the game's dynamic depends on an unknown value that belongs to a finite set. The solution of the incentive strategy is computed in terms of the worst-case scenario, of the team's optimal solution. Based on the Robust Maximum Principle, the new incentive is presented in the form of a mini-max feedback control. Two numerical examples illustrate the effectiveness of the approach. [ABSTRACT FROM AUTHOR]

This paper presents a solution to a robust optimal regulation problem for a nonlinear polynomial system affected by parametric and matched uncertainties, which is based only on partial state information. The parameters describing the dynamics of the nonlinear polynomial plant depend on a vector of unknown parameters, which belongs to a finite parametric set, and the application of a certain control input is associated with the worst or least favourable value of the unknown parameter. A high-order sliding mode state reconstructor is designed for the nonlinear plant in such a way that the previously designed control can be applied for a system with incomplete information. Additionally, the matched uncertainty is also compensated by means of the same output-based regulator. The obtained algorithm is applied to control an uncertain nonlinear inductor circuit of the third order and a mechanical pendulum of the third order, successfully verifying the effectiveness of the developed approach. [ABSTRACT FROM PUBLISHER]