In this research paper, a recent robust control scheme was proposed and designed for a VSbW (vehicle steer-by-wire) system. Using an integral sliding mode control (ISMC) design based on barrier function (ISMCbf) could improve the robustness of ISMCs. This control scheme, due to the characteristics of the barrier function, can improve the robustness of the proposed controller better than that based on the conventional SMC or integral SMC (ISMC). The ISMCbf scheme exhibits all the benefits of the conventional ISMC with the addition of two main advantages: it does not require prior knowledge of perturbation bounds or their derivatives, and it can effectively eliminate the chattering phenomenon associated with the classical ISMC due to the smooth characteristics of the barrier function. On the other hand, in terms of the design implementation, the ISMCbf is simpler than the ISMC. In this study, the mathematical dynamical model of the VSbW plant was first presented. Then, the control design of the ISMCbf scheme was developed. The numerical results showed that the proposed scheme is superior to the conventional ISMC. The superiority of the proposed ISMCbf controller versus the classical ISM has been evaluated under three different uncertain conditions, and three scenarios can be deduced: a slalom path, quick steering, and shock disturbance rejection. Furthermore, a comparative analysis with other controllers from the literature has further been established to show the effectiveness of the proposed ISMCbf.

The Electronic Throttle Valve (ETV) is the core part of automotive engines which are recently used in control-by-wire cars. The estimation of its states and uncertainty is instructive for control applications. This study presents the design of Extended State Observer (ESO) for estimating the states and uncertainties of Electronic Throttle Valve (ETV). Two versions of ESOs have been proposed for estimation: Linear ESO (LESO) and Nonlinear ESO (NESO). The model of ETV is firstly developed and extended in state variable form such that the extended state stands for the uncertainty in system parameters. The design of both structures of ESOs are developed and a comparison study has been conducted to show the effectiveness of the proposed observers. Numerical simulation has been conducted to assess the performance of observers in estimating the states and uncertainties of ETV. The simulated results showed that both full order and reduced order models of ETV have the same transient characteristics. Moreover, the effectiveness of two versions of observers has been examined based on Root Mean Square of Error (RMSE) indicator. The results showed that the NESO has less estimation errors for both states and uncertainties than LESO.

In leader-follower Stackelberg games, the leader determines and announces its strategy first by anticipating the follower’s reaction function, and the follower determines its strategy as a best response to the leader’s strategy. Thus, there is a perceived advantage in assuming the role of leader in a Stackelberg game. When the roles of the players are not determined a priori, both players must mutually agree on the selection of the leader. Such an agreement is possible only if the players realise that they are both better off with the agreed selection of leader as compared to when the other player is selected as leader. In games with parameter uncertainty, the availability of this option depends on the parameter space over which the game is defined. In this paper, we describe the partitioning of the parameter space to characterise when a Stackelberg solution based on an agreed leader selection exists and when it does not. The resulting partition can then be used to determine the probability of occurrence of all possible games where agreement can and cannot be reached. We illustrate the results using two examples.

In this paper, we consider control systems that are controlled by multiple controllers each having its own objective function. The Nash and leader-follower Stackelberg options for designing the controls are considered. These control options are heavily used as decision options in non-zero sum differential game theory. In order to reap many of the benefits of feedback, the resulting designs are best implemented as closed-loop controls. However, closed-loop controls require continuous measurements of the system's state vector, which may be expensive or even impossible in many cases. As an alternative, in this paper we consider a sampled closed-loop implementation. Such an implementation requires measurements of the state vector only at pre-specified instants of time, and hence is much more practical and cost effective when compared to the continuous closed-loop implementation. We derive the necessary conditions for the general linear quadratic problem and develop the solutions for the Nash and Stackelberg controls in detail for the scalar case. An example of a control system with two controllers and state measurements available at integer multiples of 10% of the total interval of control is presented to illustrate the results.