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.

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 article 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.

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. In addition, 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 subdynamics, the vehicle attitude subdynamics, and the manipulator subdynamics. 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.

This article proposes a framework for adaptive synchronization of uncertain underactuated Euler-Lagrange (EL) agents. The designed distributed controller can handle both state-dependent uncertain system dynamics terms and state-dependent uncertain interconnection terms among neighboring agents. No structural knowledge of such terms is required other than the standard properties of EL systems (positive definite mass matrix, bounded gravity, velocity-dependent friction bound, etc.). The study of stability relies on a suitable analysis of the nonactuated and the actuated synchronization errors, resulting in stable error dynamics perturbed by parametrized state-dependent uncertainty. This uncertainty is tackled via appropriate adaptation laws, giving stability in the uniform ultimate boundedness sense, in line with available literature on state-dependent uncertain system dynamics and/or state-dependent uncertain interconnections. An example with a network of boom cranes is used to validate the proposed approach.

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.

In this work we propose a new practical synchronization protocol for multiple Euler Lagrange (EL) systems without structural linear-in-the-parameters (LIP) knowledge of the uncertainty and where the agents can be interconnected before control design by unknown state-dependent interconnection terms. This setting is meant to overcome two standard a priori assumptions in the literature concerning uncertainty with LIP structure and absence of interaction among agents before designing the synchronization protocol. To overcome these assumptions, we propose an adaptive distributed control mechanism having the purpose of estimating the coefficients of the resulting state-dependent uncertainty structure.

This article describes an extension of the well-known model reference adaptive control (MRAC) approach. The extension relies on explicitly involving the tracking error in the feedback control law: it is shown that including this term along with its appropriate extra adaptive gain allows one to handle possibly unstable reference dynamics. Owing to its stabilizing nature, the proposed framework is referred to as model reference adaptive stabilizing control. Such an extension turns out to be particularly useful in leaderless consensus of heterogeneous uncertain agents, since the literature has discussed that leaderless adaptation may not avoid unstable closed-loop dynamics. In such consensus setting, the framework, referred to as model reference adaptive stabilizing consensus, generalizes the existing MRAC-based consensus schemes and can achieve consensus when state-of-the-art MRAC-based schemes may fail.

Piecewise-affine (PWA) approximations are widely used among hybrid modeling frameworks as a way to increase computational efficiency in nonlinear control and optimization problems. A variety of approaches to construct PWA approximations have been proposed, most of which are tailored to specific application areas by using some prior knowledge of the system in their assumptions and/or steps. In this paper, a parametric method is proposed to identify PWA approximations of nonlinear systems, without any prior knowledge of their dynamics or application requirements. The algorithm defines the regions parametrically using hyperplanes to cut the domain, and increases the number of regions iteratively until a user-defined error tolerance criterion is met. General remarks are given on the algorithm's implementation and a case study is provided to illustrate its application to vehicle dynamics.

Satisfying thermal comfort in indoor spaces is still a challenge in terms of energy saving, and several HVAC (Heating, Ventilation, and Air-Conditioning) systems have been proposed for this purpose. This paper conducts an analysis to evaluate and optimize the long-term operation of a novel HVAC system installed at The Green Village, a living lab in Delft, the Netherlands. This system comprises all-glass facades with steerable solar shades, sky windows, a climate tower equipped with Phase-Change Material (PCM), a heat recovery unit, and a heat pump. The current analysis draws on transient modeling to predict the system's behavior while relying on constrained nonlinear optimization to select the optimal design parameters (e.g. floor heat capacity and solar absorptance) and optimal operational conditions (e.g. use of PCM and heat recovery unit, aperture of sky windows and solar shadings). The goal is to schedule the control inputs to operate the system as much as possible as a passive energy system, with minimal active power all year round. The results show that the optimization can reduce the yearly heat demand by around 10.6%, with the solar shadings being the most significant component to be optimized. Furthermore, the optimized system is capable to supply 58% of the annual thermal demand passively – In this case, an auxiliary thermal demand of only 27 kWh/m²/year is required, which may qualify the system as a low-energy building.

We revisit distributed sampled-data consensus problems from a scalability point of view. Existing solutions in the literature for estimating the maximum sampling interval that preserves stability rely on the Lyapunov functional method. With this method, the overall closed-loop system (i.e. the overall network of agents) is treated as a time-delayed system. Here, a critical point is the scalability of the resulting stability conditions: in fact, the size of the LMIs to be solved depends on the size of the network. In contrast with this method, an easy-to-use and scalable method is presented, with stability conditions that are independent on the size of the network. It is shown that the proposed method can handle linear and Lipschitz nonlinear multiagent systems with both aperiodic time-triggered and event-triggered control in a unified way. Numerical examples show the efficiency of the proposed approach and the tightness of the estimated maximum sampling interval.

The vector field method was originally proposed to guide a single fixed-wing Unmanned Aerial Vehicle (UAV) towards a desired path. In this work, a non-uniform vector field method is proposed that changes in both magnitude and direction, for the purpose of achieving formations of UAVs. As compared to related work in the literature, the proposed formation control law does not need to assume absence of wind. That is, due to the effect of the wind on the UAV, one can handle the UAV air speed being different from its ground speed, and the UAV heading angle being different from its course angle. Stability of the proposed formation method is analyzed via Lyapunov stability theory, and validations are carried out in software-in-the-loop and hardware-in-the-loop comparative experiments. Note to Practitioners - The software-in-the-loop and hardware-in-the-loop experiments, which are done with PX4 autopilot software and hardware, show that the proposed method can be implemented on board of UAVs and integrated with the control architecture of existing autopilot suites. Comparisons with standard formation algorithms show that the proposed method is effective in achieving formation in different path scenarios.

Actor-critic (AC) cooperative multiagent reinforcement learning (MARL) over directed graphs is studied in this article. The goal of the agents in MARL is to maximize the globally averaged return in a distributed way, i.e., each agent can only exchange information with its neighboring agents. AC methods proposed in the literature require the communication graphs to be undirected and the weight matrices to be doubly stochastic (more precisely, the weight matrices are row stochastic and their expectation are column stochastic). Differently from these methods, we propose a distributed AC algorithm for MARL over directed graph with fixed topology that only requires the weight matrix to be row stochastic. Then, we also study the MARL over directed graphs (possibly not connected) with changing topologies, proposing a different distributed AC algorithm based on the push-sum protocol that only requires the weight matrices to be column stochastic. Convergence of the proposed algorithms is proven for linear function approximation of the action value function. Simulations are presented to demonstrate the effectiveness of the proposed algorithms.

Controlling the operation of HVAC (Heating, Ventilation, and Air-Conditioning) systems is arguably the most effective way to reach desired indoor conditions in buildings. Nevertheless, such control may involve complex dynamics when dealing with passive energy technologies. In this paper, we focus on maximizing the passive operation of HVAC in a novel low-energy building design by means of Model Predictive Control (MPC). The low-energy building design, located in The Green Village, consists of a thermal chimney and solar shades over all-glass facades to provide the required indoor air conditioning as passively as possible. The MPC controller is based on a transient grey box model and a hierarchical control architecture to satisfy thermal comfort while minimizing the active energy requirements. Using sensor data collected from the actual building in April and May 2021, the grey box model shows a good agreement with the measurements, since the variance accounted for is 90% in most cases. Moreover, via a comparative study among different MPC architectures we show that managing the distinct transient response of each component (shades and chimney) is the best for successful overall performance – e.g. considering linear agents for shading and nonlinear agents for ventilation. The hierarchical MPC architecture established outperforms the standard ones by 22.7% in terms of control performance. We also compare the proposed MPC approach against the rule-based control method currently implemented in the actual building, which indicates that MPC demands about 78% less active energy, highlighting the proposed optimization-based control approach.

This paper addresses distributed adaptive optimal resource allocation problems over weight-balanced digraphs. By leveraging state-of-the-art adaptive coupling designs for multiagent systems, two adaptive algorithms are proposed, namely a directed-spanning-tree-based algorithm and a node-based algorithm. The benefits of these algorithms are that they require neither sufficiently small or unitary step sizes, nor global knowledge of Laplacian eigenvalues, which are widely required in the literature. It is shown that both algorithms belong to a class of uncertain saddle-point dynamics, which can be tackled by repeatedly adopting the Peter-Paul inequality in the framework of Lyapunov theory. Thanks to this new viewpoint, global asymptotic convergence of both algorithms can be proven in a unified way. The effectiveness of the proposed algorithms is validated through numerical simulations and case studies in IEEE 30-bus and 118-bus power systems.

Practical tracking results have been reported in the literature for high-order odd-rational-power nonlinear dynamics (a chain of integrators whose power is the ratio of odd integers). Asymptotic tracking remains an open problem for such dynamics. This note gives a positive answer to this problem in the framework of prescribed performance control, without approximation structures (neural networks, fuzzy logic, etc.) being involved in the control design. The unknown system uncertainties are first transformed to unknown but bounded terms using barrier Lyapunov functions, and then these terms are compensated by appropriate adaptation laws. A method is also proposed to extract the control terms in a linear-like fashion during the control design, which overcomes the difficulty that virtual or actual control signals appear in a nonaffine manner. A practical poppet valve system is used to validate the effectiveness of the theoretical findings.

This article 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 article, group model learning is achieved for Euler-Lagrange dynamics over directed networks in the presence of persistent unknown disturbances.

This paper addresses distributed and robust leaderless consensus control for a class of uncertain multiagent systems with matched unknown nonlinearities and disturbances. The problem is challenging due to the lack of a leader (reference signal), the large uncertainties in agent dynamics, and the asymmetric communications among the agents. A novel neural network embedded model reference adaptive consensus (NN-MRACon) framework is proposed, which bridges NN and MRACon by means of nonsmooth control. Asymptotic consensus is proved based on robust analysis and input-to-state stability theory. Numerical examples on networks of second-order integrators and two-mass-spring systems are included to validate the effectiveness of NN-MRACon.

Prescribed-performance control (PPC) for high-power dynamics with time-varying unknown control coefficients requires to address two open problems: (a) given a Nussbaum function, which properties hold for the power of the Nussbaum function? (b) to avoid high gains, how to design a switching gain that increases only when the tracking error is close to violate the performance bounds? To address the first problem, we show with a counterexample and a positive example that only some Nussbaum functions are suited to handle time-varying unknown control coefficients for high-power dynamics. To address the second problem, we propose a new switching conditional inequality.