We consider the online control problem with an unknown linear dynamical system in the presence of adversarial perturbations and adversarial convex loss functions. Although the problem is widely studied in model-based ...
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We consider the problem of black-box control: the task of controlling an unknown linear time-invariant dynamical system from a single trajectory without a stabilizing controller. Under the assumption that the system i...
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We consider the problem of black-box control: the task of controlling an unknown linear time-invariant dynamical system from a single trajectory without a stabilizing controller. Under the assumption that the system is controllable, we give the first efficient algorithm that attains sublinear regret under the setting of online nonstochastic control. This resolves an open problem since the work of Abbasi-Yadkori and Szepesvari (2011) on the stochastic black-box LQR problem, and in a more general setting that allows for adversarial perturbations and adversarially chosen changing convex loss functions. We give finite-time regret bounds for our algorithm on the order of 2(poly(d)) + (O) over tilde (poly(d)T-2/3) for general nonstochastic control, and 2(poly(d)) + (O) over tilde (poly(d)root T) for black-box LQR. To complete the picture, we investigate the complexity of the online black-box control problem and give a matching regret lower bound of 2(Omega(d)), showing that the exponential cost is inevitable. This lower bound holds even in the noiseless setting, and applies to any, randomized or deterministic, blackbox control method.
The risk-neutral LQR controller is optimal for stochastic linear dynamical systems. However, the classical optimal controller performs inefficiently in the presence of low-probability yet statistically significant (ri...
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In the paper, the requirements for aircraft guidance methods are considered. It is noted that the existing methods of optimization of linear control systems based mainly on the minimization of quadratic functionals of...
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In the paper, the requirements for aircraft guidance methods are considered. It is noted that the existing methods of optimization of linear control systems based mainly on the minimization of quadratic functionals of quality do not allow providing the set of requirements for interception systems of aerial objects. It is proposed to use new local quadratic-biquadratic quality functionals, whose minimization makes it possible to obtain more general linear-cubic control laws that are adequate for modern requirements. The biquadratic terminal part of the functional contains fourth-degree summands. An example of the synthesis of a specific guidance method is considered and analyzed.
Although optimal control problems for linearsystems have been profoundly investigated in the past more than 50 years, the issue of numerical approximations and precise error analyses remains challenging due the bang-...
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ISBN:
(纸本)9783662438800;9783662438794
Although optimal control problems for linearsystems have been profoundly investigated in the past more than 50 years, the issue of numerical approximations and precise error analyses remains challenging due the bang-bang structure of the optimal controls. Based on a recent paper by M. Quincampoix and V. M. Veliov on metric regularity of the optimality conditions for control problems of linearsystems the paper presents new error estimates for the Euler discretization scheme applied to such problems. It turns out that the accuracy of the Euler method depends on the "controllability index" associated with the optimal solution, and a sharp error estimate is given in terms of this index. The result extends and strengthens in several directions some recently published ones.
This paper focuses on the problem of adaptive integral sliding mode control (ISMC) with dissipativity for a type of complex non-linear system represented by Takagi-Sugeno (T-S) fuzzy descriptor models. First, T-S fuzz...
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This paper focuses on the problem of adaptive integral sliding mode control (ISMC) with dissipativity for a type of complex non-linear system represented by Takagi-Sugeno (T-S) fuzzy descriptor models. First, T-S fuzzy descriptor systems with different derivative matrices are transformed into augmented systems that have the same properties as the original systems, and an integral sliding mode surface function is designed considering the descriptor matrices. Then, based on the dissipativity theory and the non-parallel distributed compensation (non-PDC) method, ISMC strategies and dissipativity-based ISMC strategies are proposed, and the system uncertainties and external disturbances with unknown upper bounds are addressed with an adaptive controller. According to the Lyapunov theory and the dissipativity theory, a fuzzy Lyapunov function is designed, and the obtained criteria are presented in the form of strict linear matrix inequalities (LMIs);this approach guarantees that the closed-loop system is asymptotically stable and strictly (Q,R,S)-alpha$(\mathcal{Q},\mathcal{R},\mathcal{S}) - {{\alpha}}$ dissipative. Moreover, the controller gain matrices and Lyapunov matrices are decoupled by introducing the corresponding auxiliary variables and employing Finsler's lemma. Finally, two examples are provided to illustrate the effectiveness and merit of the proposed method.
While the optimization landscape of policy gradient methods has been recently investigated for partially observed linearsystems in terms of both static output feedback and dynamical controllers, they only provide con...
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We concern with the classification problem of generalized linear control systems, which might be useful for some engineering applications. Inspired by the work of Shayman and Zhou in 1987, we give the definition of li...
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This paper deals with the problem of designing a sampled-data state feedback control law for continuous-time linear control systems subject to uniform input quantization. The sampled-data state feedback is designed in...
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linear time-varying (LTV) systems are widely used for modeling real-world dynamical systems due to their generality and simplicity. Providing stability guarantees for LTV systems is one of the central problems in cont...
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