We consider stabilization and performance optimization of non-linear controlled systems, where the non-linearity satisfies a sector constraint asymptotically. This leads to optimization of the closed loop peak-to-peak system norm subject to $H_\infty$-performance constraints. Non-linear controlled systems tuned successfully by this novel approach are locally exponentially stable and globally BIBO-stable.
This paper studies the mixed $H_-/H_{\infty}$ fault detection filtering of Itô-type nonlinear stochastic systems. Mixed $H_-/H_{\infty}$ filtering combines the system robustness to the external disturbance and the sensitivity to the fault of the residual signal. Firstly, for Itô-type affine nonlinear stochastic systems, some sufficient criteria are obtained for the existence of $H_-/H_{\infty}$ filter in terms of Hamilton-Jacobi inequalities (HJIs). Secondly, for a class of quasi-linear Itô systems, a sufficient condition is given for the existence of $H_-/H_{\infty}$ filter by means of linear…
For a particular class of planar dynamics that are linear with respect to the control variable, we show that the feedback strategy ''null-singular null'' is minimizing the maximum of a coordinate over infinite horizon, under a L 1 budget constraint on the control. Moreover, we characterize the optimal cost as a function of the budget. The proof is based on an unusual use of the clock form. This result generalizes the one obtained formerly for the SIR epidemiological model to more general Kolmogorov dynamics, that we illustrate on other biological models.
This paper revisits the robustness analysis and distributed ${ H}_\infty$ controller design for the platooning of connected vehicles. Recently, the relevant result subjected to the undirected topology has been studied, in the light of the symmetry of Laplace matrix. It is well known that the same problem is more challenging for the \emph{directed} topology, since the Laplace matrix ceases to be symmetric. In this paper, the problem is solved by introducing more weighting parameters and setting suitable values for them. Then we show that the introduced weighting parameters lead to a positive ef…
Mixed norms that promote structured sparsity have numerous applications in signal processing and machine learning problems. In this work, we present a new algorithm, based on a Newton root search technique, for computing the projection onto the $\ell_{\infty,1}$ ball, which has found application in cognitive neuroscience and classification tasks. Numerical simulations show that our proposed method is between 8 and 10 times faster on average, and up to 20 times faster for very sparse solutions, than the previous state of the art. Tests on real functional magnetic resonance image data show that,…
University of Illinois at Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）
Direct policy search has been widely applied in modern reinforcement learning and continuous control. However, the theoretical properties of direct policy search on nonsmooth robust control synthesis have not been fully understood. The optimal $\mathcal{H}_\infty$ control framework aims at designing a policy to minimize the closed-loop $\mathcal{H}_\infty$ norm, and is arguably the most fundamental robust control paradigm. In this work, we show that direct policy search is guaranteed to find the global solution of the robust $\mathcal{H}_\infty$ state-feedback control design problem. Notice th…
This paper investigates state feedback control laws for Markov jump linear systems with state and mode-observation delays. An assumption in this study is that the delay of mode observation obeys an exponential distribution. Also, we raise an unknown time-varying state delay applied in the composition of the state feedback controller. A method of remodeling the closed-loop system as a standard Markov jump linear system with state delay is shown. Furthermore, on the basis of this remodeling, several Linear Matrix Inequalities (LMI) for designing feedback gains for stabilization and mixed $H_2/H_…
This paper considers the H\infty-optimal estimation problem for linear systems with multiple delays in states, output, and disturbances. First, we formulate the H\infty-optimal estimation problem in the Delay-Differential Equation (DDE) framework. Next, we construct an equivalent Partial Integral Equation (PIE) representation of the optimal estimator design framework. We then show that in the PIE framework, the H\infty-optimal estimator synthesis problem can be posed as a Linear PI Inequality (LPI). LPIs are a generalization of LMIs to the algebra of Partial Integral (PI) operators and can be …
The local stability of the solution map to a parametric boundary control problem governed by semilinear elliptic equations with finite mixed pointwise constraints is considered in this paper. We prove that the solution map is locally Hölder continuous in $L^\infty-$norm of control variable when the strictly nonnegative second-order optimality conditions are satisfied for the unperturbed problem.
Structured output feedback controller synthesis is an exciting recent concept in modern control design, which bridges between theory and practice in so far as it allows for the first time to apply sophisticated mathematical design paradigms like $H_\infty$- or $H_2$-control within control architectures preferred by practitioners. The new approach to structured $H_\infty$-control, developed by the authors during the past decade, is rooted in a change of paradigm in the synthesis algorithms. Structured design is no longer be based on solving algebraic Riccati equations or matrix inequalities. In…
In this paper, we study mixed traffic systems that move along a single-lane ring-road or open-road. The traffic flow forms a platoon, which includes a number of heterogeneous human-driven vehicles (HDVs) together with only one connected and automated vehicle (CAV) that receives information from several neighbors. The dynamics of HDVs are assumed to follow the optimal velocity model (OVM), and the acceleration of the single CAV is directly controlled by a dynamical output-feedback controller. The ultimate goal of this work is to present a robust control strategy that can smoothen the traffic fl…
Impedance control of a cable-driven SEA with mixed $H_2/H_\infty$ synthesis
Institute of Robotics and Automatic Information Systems, Nankai University（机器人与自动信息系统研究所，南开大学）；Tianjin Key Laboratory of Intelligent Robotics, Nankai University（天津智能机器人重点实验室，南开大学）
Georgia Institute of Technology（佐治亚理工学院）；University of California, Santa Barbara（加利福尼亚大学圣塔芭芭拉分校）
Implicit neural networks are a general class of learning models that replace the layers in traditional feedforward models with implicit algebraic equations. Compared to traditional learning models, implicit networks offer competitive performance and reduced memory consumption. However, they can remain brittle with respect to input adversarial perturbations. This paper proposes a theoretical and computational framework for robustness verification of implicit neural networks; our framework blends together mixed monotone systems theory and contraction theory. First, given an implicit neural netwo…
The Johns Hopkins University（约翰斯·霍普金斯大学）；University of Illinois at Urbana Champaign（伊利诺伊大学厄巴纳-香槟分校）
Proximal operators are of particular interest in optimization problems dealing with non-smooth objectives because in many practical cases they lead to optimization algorithms whose updates can be computed in closed form or very efficiently. A well-known example is the proximal operator of the vector $\ell_1$ norm, which is given by the soft-thresholding operator. In this paper we study the proximal operator of the mixed $\ell_{1,\infty}$ matrix norm and show that it can be computed in closed form by applying the well-known soft-thresholding operator to each column of the matrix. However, unlik…
