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This brief is concerned with the robust adaptive tracking control problem of quadrotors. Considering the practicality of control laws to be designed, the self-tuning regulator (STR) for discrete-time systems is employed as our inner loop adaptive tracking mechanism and the classical proportional–integral (PI) control is designed for the outer loop to guarantee the robustness of the whole system. The main contributions of our work include: 1) we design the control laws for the actuator inputs (pulsewidth modulation signals) directly, which removes the need to measure the motor speeds and 2) the proposed PI-STR method can reduce the large overshoot of a single STR and retain the adaptability of the STR and the robustness of the PI control simultaneously. Furthermore, the outer loop PI controller and inner loop STR can easily be implemented in the digital form. The stability analysis is also provided. Simulations indicate that the PI-STR-based control structure can cope with the situations where vehicles are disturbed or have time-varying parameters. Our preliminary experiments show its practicality. [ABSTRACT FROM AUTHOR]

It is well known that discrete-time linear systems can be stabilized by a least-squares (LS) based self-tuning regulator (STR), as long as noises are absent. However, this note shows that once the discrete-time linear systems are disturbed, the LS-based STR is always running the risk of failing in stabilizing the systems, no matter how small the noises are. [ABSTRACT FROM AUTHOR]

In this paper, two new pairs of dual continuous-time algebraic Riccati equations (CAREs) and dual discrete-time algebraic Riccati equations (DAREs) are proposed. The dual DAREs are first studied with some nonsingularity assumptions on the system matrix and the parameter matrix. Then, in the case of singular matrices, a generalised inverse is introduced to deal with the dual DARE problem. These dual AREs can easily lead us to an iterative procedure for finding the anti-stabilising solutions, especially to DARE, by means of that for the stabilising solutions. Furthermore, we provide the counterpart results on the set of all solutions to DARE inspired by the results for CARE. Two examples are presented to illustrate the theoretical results. [ABSTRACT FROM AUTHOR]

Abstract: It is fairly well known that there are fundamental differences between adaptive control of continuous-time and discrete-time nonlinear systems. In fact, even for the seemingly simple single-input single-output control system with a scalar unknown parameter and noise disturbance , and with a known function having possible nonlinear growth rate characterized by with , the necessary and sufficient condition for the system to be globally stabilizable by adaptive feedback is . This was first found and proved by for the Gaussian white noise case, and then proved by for the bounded noise case. Subsequently, a number of other types of “critical values” and “impossibility theorems” on the maximum capability of adaptive feedback were also found, mainly for systems with known control parameter as in the above model. In this paper, we will study the above basic model again but with additional unknown control parameter , i.e.,  is replaced by in the above model. Interestingly, it turns out that the system is globally stabilizable if and only if . This is a new critical theorem for adaptive nonlinear stabilization, which has meaningful implications for the control of more general uncertain nonlinear systems. [Copyright &y& Elsevier]

Abstract: We consider adaptive control of discrete-time nonlinear systems with a single unknown parameter in this paper. We demonstrate that the necessary and sufficient condition for the existence of a feedback stabilizer that is robust to bounded noise is that the nonlinear growth rate of the system dynamics is less than 4. This result further confirms the conclusion of Guo [On critical stability of discrete-time adaptive nonlinear control, IEEE Trans. Automat. Control 42 (1997) 1488–1499] which addresses unbounded noise in a stochastic setting. Also in our worst-case approach, we find that much simpler adaptive stabilizers can be constructed when the nonlinear growth rate is less than 4. [Copyright &y& Elsevier]

This paper studies the identification of discrete-time nonlinear parameterized control systems in given experiments. A necessary and sufficient condition of the closed-loop identifiability is established for the stable experiments and an algorithm is proposed to estimate the parameter. The estimates are shown to be strongly consistent with the convergence rate explicitly computed under some simple algebraic condition. [ABSTRACT FROM AUTHOR]