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PieceWise Affine (PWA) approximations for nonlinear functions have been extensively used for tractable, computationally efficient control of nonlinear systems. However, reaching a desired approximation accuracy without prior information about the behavior of the nonlinear systems remains a challenge in the function approximation and control literature. As the name suggests, PWA approximation aims at approximating a nonlinear function or system by dividing the domain into multiple subregions where the nonlinear function or dynamics is approximated locally by an affine function also called local mode. Without prior knowledge of the form of the nonlinearity, the required number of modes, the locations of the subregions, and the local approximations need to be optimized simultaneously, which becomes highly complex for large-scale systems with multi-dimensional nonlinear functions. This paper introduces a novel approach for PWA approximation of multi-dimensional nonlinear systems, utilizing a hinging hyperplane formalism for cut-based partitioning of the domain. The complexity of the PWA approximation is iteratively increased until reaching the desired accuracy level. Further, the tractable cut definitions allow for different forms of subregions, as well as the ability to impose continuity constraints on the PWA approximation. The methodology is explained via multiple examples and its performance is compared to two existing approaches through case studies, showcasing its efficacy., Comment: 9 pages, 4 figures, submitted to journal

Successful aerial manipulation largely depends on how effectively a controller can tackle the coupling dynamic forces between the aerial vehicle and the manipulator. However, this control problem has remained largely unsolved as the existing control approaches either require precise knowledge of the aerial vehicle/manipulator inertial couplings, or neglect the state-dependent uncertainties especially arising during the interaction phase. This work proposes an adaptive control solution to overcome this long standing control challenge without any a priori knowledge of the coupling dynamic terms. Additionally, in contrast to the existing adaptive control solutions, the proposed control framework is modular, that is, it allows independent tuning of the adaptive gains for the vehicle position sub-dynamics, the vehicle attitude sub-dynamics, and the manipulator sub-dynamics. Stability of the closed loop under the proposed scheme is derived analytically, and real-time experiments validate the effectiveness of the proposed scheme over the state-of-the-art approaches.

Nonlinear Programs (NLPs) are prevalent in optimization-based control of nonlinear systems. Solving general NLPs is computationally expensive, necessitating the development of fast hardware or tractable suboptimal approximations. This paper investigates the sensitivity of the solutions of NLPs with polytopic constraints when the nonlinear continuous objective function is approximated by a PieceWise-Affine (PWA) counterpart. By leveraging perturbation analysis using a convex modulus, we derive guaranteed bounds on the distance between the optimal solution of the original polytopically-constrained NLP and that of its approximated formulation. Our approach aids in determining criteria for achieving desired solution bounds. Two case studies on the Eggholder function and nonlinear model predictive control of an inverted pendulum demonstrate the theoretical results., Comment: 6 pages, 4 figures, accepted for publication in IEEE Control Systems Letters

Uncertainty in the behavior of other traffic participants is a crucial factor in collision avoidance for automated driving; here, stochastic metrics could avoid overly conservative decisions. This paper introduces a Stochastic Model Predictive Control (SMPC) planner for emergency collision avoidance in highway scenarios to proactively minimize collision risk while ensuring safety through chance constraints. To guarantee that the emergency trajectory can be attained, we incorporate nonlinear tire dynamics in the prediction model of the ego vehicle. Further, we exploit Max-Min-Plus-Scaling (MMPS) approximations of the nonlinearities to avoid conservatism, enforce proactive collision avoidance, and improve computational efficiency in terms of performance and speed. Consequently, our contributions include integrating a dynamic ego vehicle model into the SMPC planner, introducing the MMPS approximation for real-time implementation in emergency scenarios, and integrating SMPC with hybridized chance constraints and risk minimization. We evaluate our SMPC formulation in terms of proactivity and efficiency in various hazardous scenarios. Moreover, we demonstrate the effectiveness of our proposed approach by comparing it with a state-of-the-art SMPC planner and we validate that the generated trajectories can be attained using a high-fidelity vehicle model in IPG CarMaker., Comment: 14 pages, 11 figures, submitted to IEEE Transactions on Control Systems Technology

The objective of model reference control is to design a controller that regulates the system's behavior so as to match a specified reference model. This paper investigates necessary and sufficient conditions for model reference control from a data-driven perspective, when only a set of data generated by the system is utilized to directly accomplish the matching. Noiseless and noisy data settings are both considered. Notably, all methods we propose build on the concept of data informativity and do not rely on persistently exciting data.

Optimization-based approaches such as Model Predictive Control (MPC) are promising approaches in proactive control for safety-critical applications with changing environments such as automated driving systems. However, the computational complexity of the MPC optimization problem coupled with the need for real-time control in hazardous scenarios is the main bottleneck in realization of automation levels four and five for driving systems. In this paper, we construct hybrid formulations of the nonlinear MPC problem for tracking control during emergency evasive maneuvers and assess their computational efficiency in terms of accuracy and solution time. To hybridize the MPC problem, we combine three hybrid approximations of the prediction model and four approximations of the nonlinear stability and tire saturation constraints and simulate the closed-loop behavior of the resulting controllers during five emergency maneuvers for different prediction horizons. Further, we compare the robustness of the controllers in the presence of friction uncertainty as well to assess the accuracy-time trade-off in cases where the friction of the road is either unknown or has an offset error with respect to the prediction model. This robustness is studied for different levels of friction uncertainty, as well as investigated with respect to the proximity to the vehicle handling limits. We show that the hybridization of the MPC problem is an efficient approach for real-time implementation of MPC during emergency evasive maneuvers, paving the way for implementation of high levels of automation., Comment: 13 pages, 7 figures, submitted to Journal

Despite the extensive application of nonlinear Model Predictive Control (MPC) in automated driving, balancing its computational efficiency with respect to the control performance and constraint satisfaction remains a challenge in emergency scenarios: in such situations, sub-optimal but computationally fast responses are more valuable than optimal responses obtained after long computations. In this paper, we introduce a hybridization approach for efficient approximation of nonlinear vehicle dynamics and non-convex constraints using a hybrid systems modeling framework. Hybridization allows to reformulate the nonlinear MPC problem during emergency evasive maneuvers as a hybrid MPC problem. In this regard, Max-Min-Plus-Scaling (MMPS) hybrid modeling is used to approximate the nonlinear vehicle dynamics. Meanwhile, different formulations for constraint approximation are presented, and various grid-generation methods are compared to solve these approximation problems. Among these, two novel grid types are introduced to structurally include the influence of the system dynamics on the grid point distributions in the state domain. Overall, the work presents and compares three hybrid models and four hybrid constraints for efficient MPC synthesis and offers guidelines for implementation of the presented hybridization framework in other applications., Comment: 13 pages, 7 figures, submitted to journal

This work proposes provably-correct self-organizing strategies for platoons of heterogeneous vehicles. We refer to self-organization as the capability of a platoon to autonomously homogenize to a common group behavior. We show that self-organization promotes resilience to acceleration limits and communication failures, i.e., homogenizing to a common group behavior makes the platoon recover from these causes of impairments. In the presence of acceleration limits, resilience is achieved by self-organizing to a common constrained group behavior that prevents the vehicles from hitting their acceleration limits. In the presence of communication failures, resilience is achieved by self-organizing to a common group observer to estimate the missing information. Stability of the self-organization mechanism is studied analytically, and correctness with respect to traffic actions (e.g. emergency braking, cut-in, merging) is realized through a provably-correct safety layer. Numerical validations via the platooning toolbox OpenCDA in CARLA and via the CommonRoad platform confirm improved performance through self-organization and the provably-correct safety layer.

This paper studies the leaderless consensus problem of {heterogeneous} multiple networked Euler-Lagrange systems subject to persistent disturbances with unknown constant biases, amplitudes, initial phases, and frequencies. The main characteristic of this study is that none of the agents has information of a common reference model or of a common reference trajectory. Therefore, the agents must simultaneously and in a distributed way: achieve consensus to a common reference model (group model); achieve consensus to a common reference trajectory; {and} reject the unknown disturbances. We show that this is possible via a suitable combination of techniques of distributed `observers', internal model principle, and adaptive regulation. The proposed design generalizes recent results on group model learning, which have been studied for linear agents over undirected networks. In this work, group model learning is achieved for Euler-Lagrange dynamics over directed networks in the presence of persistent unknown disturbances.