This paper provides a constructive passivity-based control approach to solve the set-point regulation problem for input-affine continuous nonlinear systems while considering saturation in the inputs. As customarily in passivity-based control, the methodology consists of two steps: energy shaping and damping injection. In terms of applicability, the proposed controllers have two advantages concerning other passivity-based control techniques: (i) the energy shaping is carried out without solving partial differential equations, and (ii) the damping injection is performed without measuring the passive output. The proposed methodology is suitable to control a broad range of physical systems, e.g., mechanical, electrical, and electro-mechanical systems. We illustrate the applicability of the technique by designing controllers for systems in different physical domains, where we validate the analytical results via simulations and experiments.
This paper proposes a new deep learning (DL) based model-free robust method for bulk system on-line load restoration with high penetration of wind power. Inspired by the iterative calculation of the two-stage robust load restoration model, the deep neural network (DNN) and deep convolutional neural network (CNN) are respectively designed to find the worst-case system condition of a load pickup decision and evaluate the corresponding security. In order to find the optimal result within a limited number of checks, a load pickup checklist generation (LPCG) algorithm is developed to ensure the optimality. Then, the fast robust load restoration strategy acquisition is achieved based on the designed one-line strategy generation (OSG) algorithm. The proposed method finds the optimal result in a model-free way, holds the robustness to handle uncertainties, and provides real-time computation. It can completely replace conventional robust optimization and supports on-line robust load restoration which better satisfies the changeable restoration process. The effectiveness of the proposed method is validated using the IEEE 30-bus system and the IEEE 118-bus system, showing high computational efficiency and considerable accuracy.
A robust controller is specified, and the stability bounds of the uncertain closed-loop system are determined using the small gain, circle, positive real, and Popov criteria. A graphical approach is employed in order to demonstrate the ease with which the above robustness tests can be carried out on a problem of practical interest. A significant improvement in stability bounds is observed as the analysis moves from the small gain test to the circle, positive real, and Popov tests. In particular, small gain analysis results in the most conservative robust stability bounds, while Popov analysis yields significantly less conservative bounds. This is because traditional small gain type tests allow the uncertainty to be arbitrarily time-varying, whereas Popov analysis restricts the uncertainty to be constant, real parametric uncertainty. Therefore, the results reported here indicate the conservatism associated with small gain analysis, and the effectiveness of Popov analysis, in gauging robust stability in the presence of constant, real parametric uncertainty.
Radio access network (RAN) slicing is an important part of network slicing in 5G. The evolving network architecture requires the orchestration of multiple network resources such as radio and cache resources. In recent years, machine learning (ML) techniques have been widely applied for network slicing. However, most existing works do not take advantage of the knowledge transfer capability in ML. In this paper, we propose a transfer reinforcement learning (TRL) scheme for joint radio and cache resources allocation to serve 5G RAN slicing.We first define a hierarchical architecture for the joint resources allocation. Then we propose two TRL algorithms: Q-value transfer reinforcement learning (QTRL) and action selection transfer reinforcement learning (ASTRL). In the proposed schemes, learner agents utilize the expert agents knowledge to improve their performance on target tasks. The proposed algorithms are compared with both the model-free Q-learning and the model-based priority proportional fairness and time-to-live (PPF-TTL) algorithms. Compared with Q-learning, QTRL and ASTRL present 23.9% lower delay for Ultra Reliable Low Latency Communications slice and 41.6% higher throughput for enhanced Mobile Broad Band slice, while achieving significantly faster convergence than Q-learning. Moreover, 40.3% lower URLLC delay and almost twice eMBB throughput are observed with respect to PPF-TTL.
In this paper we consider the problem of finding a Nash equilibrium (NE) via zeroth-order feedback information in games with merely monotone pseudogradient mapping. Based on hybrid system theory, we propose a novel extremum seeking algorithm which converges to the set of Nash equilibria in a semi-global practical sense. Finally, we present two simulation examples. The first shows that the standard extremum seeking algorithm fails, while ours succeeds in reaching NE. In the second, we simulate an allocation problem with fixed demand.
In this paper, we investigate a sparse optimal control of continuous-time stochastic systems. We adopt the dynamic programming approach and analyze the optimal control via the value function. Due to the non-smoothness of the $L^0$ cost functional, in general, the value function is not differentiable in the domain. Then, we characterize the value function as a viscosity solution to the associated Hamilton-Jacobi-Bellman (HJB) equation. Based on the result, we derive a necessary and sufficient condition for the $L^0$ optimality, which immediately gives the optimal feedback map. Especially for control-affine systems, we consider the relationship with $L^1$ optimal control problem and show an equivalence theorem.
Detection and mitigation of Byzantine behaviors in a decentralized learning setting is a daunting task, especially when the data distribution at the users is heterogeneous. As our main contribution, we propose Basil, a fast and computationally efficient Byzantine robust algorithm for decentralized training systems, which leverages a novel sequential, memory assisted and performance-based criteria for training over a logical ring while filtering the Byzantine users. In the IID dataset distribution setting, we provide the theoretical convergence guarantees of Basil, demonstrating its linear convergence rate. Furthermore, for the IID setting, we experimentally demonstrate that Basil is robust to various Byzantine attacks, including the strong Hidden attack, while providing up to ${sim}16 %$ higher test accuracy over the state-of-the-art Byzantine-resilient decentralized learning approach. Additionally, we generalize Basil to the non-IID dataset distribution setting by proposing Anonymous Cyclic Data Sharing (ACDS), a technique that allows each node to anonymously share a random fraction of its local non-sensitive dataset (e.g., landmarks images) with all other nodes. We demonstrate that Basil alongside ACDS with only $5%$ data sharing provides effective toleration of Byzantine nodes, unlike the state-of-the-art Byzantine robust algorithm that completely fails in the heterogeneous data setting. Finally, to reduce the overall latency of Basil resulting from its sequential implementation over the logical ring, we propose Basil+. In particular, Basil+ provides scalability by enabling Byzantine-robust parallel training across groups of logical rings, and at the same time, it retains the performance gains of Basil due to sequential training within each group. Furthermore, we experimentally demonstrate the scalability gains of Basil+ through different sets of experiments.
The hierarchical quadratic programming (HQP) is commonly applied to consider strict hierarchies of multi-tasks and robots physical inequality constraints during whole-body compliance. However, for the one-step HQP, the solution can oscillate when it is close to the boundary of constraints. It is because the abrupt hit of the bounds gives rise to unrealisable jerks and even infeasible solutions. This paper proposes the mixed control, which blends the single-axis model predictive control (MPC) and proportional derivate (PD) control for the whole-body compliance to overcome these deficiencies. The MPC predicts the distances between the bounds and the control target of the critical tasks, and it provides smooth and feasible solutions by prediction and optimisation in advance. However, applying MPC will inevitably increase the computation time. Therefore, to achieve a 500 Hz servo rate, the PD controllers still regulate other tasks to save computation resources. Also, we use a more efficient null space projection (NSP) whole-body controller instead of the HQP and distribute the single-axis MPCs into four CPU cores for parallel computation. Finally, we validate the desired capabilities of the proposed strategy via Simulations and the experiment on the humanoid robot Walker X.
The basic reproduction number $R_0$ is a fundamental quantity in epidemiological modeling, reflecting the typical number of secondary infections that arise from a single infected individual. While $R_0$ is widely known to scientists, policymakers, and the general public, it has received comparatively little attention in the controls community. This note provides two novel characterizations of $R_0$: a stability characterization and a geometric program characterization. The geometric program characterization allows us to write $R_0$-constrained and budget-constrained optimal resource allocation problems as geometric programs, which are easily transformed into convex optimization problems. We apply these programs to a case study of allocating vaccines and antidotes, finding that targeting $R_0$ instead of the spectral abscissa of the Jacobian matrix (a common target in the controls literature) leads to qualitatively different solutions.
In this work, we perform safety analysis of linear dynamical systems with uncertainties. Instead of computing a conservative overapproximation of the reachable set, our approach involves computing a statistical approximate reachable set. As a result, the guarantees provided by our method are probabilistic in nature. In this paper, we provide two different techniques to compute statistical approximate reachable set. We have implemented our algorithms in a python based prototype and demonstrate the applicability of our approaches on various case studies. We also provide an empirical comparison between the two proposed methods and with Flow*.
