As a special class of hybrid systems, switched systems have attracted a lot of attention in the last decade due to theoretical and practical interests. When controlling switched systems, a ubiquitous problem is the presence of large parametric uncertainties and external disturbances. However, the state of the art on adaptive and robust control of switched linear systems is not satisfactory and due to the existence of theoretical gaps between adaptive and robust control for switched linear systems and non-switched linear systems. To this end, this thesis has been successfully closed some theoretical gaps, which is divided into two parts. In the first part of this thesis, to start with, we have extended the state-of-the-art results using extended notions of dwell time and of average dwell time: mode-dependent dwell time and mode-dependent average dwell time, respectively. This gives rise to less conservative switching signals. To address the cases in which the next subsystem to be switched on is known, we propose a new time-dependent switching scheme: mode-mode-dependent dwell time, which not only exploits the information of the current subsystem, but also of the next subsystem. Subsequently, an adaptive law for uncertain switched linear systems has been introduced, which fills the theoretical gaps between adaptive control of non-switched linear systems and of switched linear systems. The proposed adaptive law and switching law based on dwell time guarantee asymptotic convergence of the tracking error to zero and, with a persistent exciting reference input, convergence of parameter estimates to nominal parameters asymptotically. To conclude the first part of this thesis, the adaptive law for switched linear systems has been modified using the ideas of parameter projection and leakage method, depending on the available a priori information: when the bounds of uncertain parameters are known, parameter projection is adopted; otherwise, the leakage method is used. The resulting adaptive closed loop system is shown to be global uniform ultimate bounded in the presence of external disturbances. In the second part of this thesis, adaptive and robust stabilization of switched linear systems have been investigated. Based on the stability conditions, adaptive stabilization of uncertain asynchronously switched systems is studied. Furthermore, in the presence of discontinuous time-varying delays, neither Krasovskii nor Razumikhin techniques can be successfully applied to adaptive stabilization of uncertain switched time-delay systems. A new adaptive control scheme for switched time-delay systems is developed that can handle impulsive behavior in states and time-varying delays with discontinuities. At the core of the proposed scheme is a Lyapunov function with a dynamically time-varying coefficient, which allows the Lyapunov function to be non-increasing at the switching instants. The control scheme substantially enlarges the class of uncertain switched systems for which the adaptive stabilization problem can be solved. Furthermore, in the presence of switching delays between a mode change and activation of its corresponding controller, enhanced stability criteria are investigated, whose novelty consists in continuity of the Lyapunov function at the switching instants and discontinuity when the system modes and controller modes are matched. The proposed Lyapunov function can be used to guarantee a finite non-weighted L2 gain for asynchronously switched systems, for which methods proposed in literature are inconclusive.@en

This paper establishes an adaptive tracking approach for linear systems with parametric uncertainties, when input measurements are quantized due to the presence of a communication network closing the control loop. In order to address the tracking problem, a novel dynamic quantizer with dynamic offset is introduced and embedded into an adaptive hybrid control strategy based on zooming mechanism. A Lyapunov-based approach is used to derive the adaptive adjustments for the control gains and for the dynamic range and dynamic offset of the quantizer: it is proven analytically that the proposed adjustments guarantee asymptotic state tracking. Quantized adaptive control of an electrohydraulic system is given as an example of the effectiveness of the designed control methodology.

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This paper studies model reference adaptive control for switched linear systems with large parametric uncertainties. An aggregate leakage approach is proposed to develop a novel adaptive law, which overcomes the state-of-the-art assumption of knowing the upper and lower bounds of the parameter uncertainty. In addition, a switching law is developed based on mode-dependent average dwell time scheme, which exploits the information of the known reference model for every subsystem, i.e., average dwell time is realized in a subsystem sense. Based on the proposed time-constraint scheme, switching signals that are less conservative than those based on dwell time and average dwell time can be designed. Global uniform ultimate boundedness of the closed-loop adaptive switched system is guaranteed. Furthermore, the tracking error is shown to be upper bounded and also an ultimate bound is presented. Simulations using NASA GTM aircraft illustrate the proposed method.

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This paper addresses the problem of asymptotic tracking for switched linear systems with parametric uncertainties and dwell-time switching, when input measurements are quantized due to the presence of a communication network closing the control loop. The problem is solved via a dynamic quantizer with dynamic offset that, embedded in a model reference adaptive control framework, allows the design of the adaptive adjustments for the control parameters and for the dynamic range and dynamic offset of the quantizer. The overall design is carried out via a Lyapunov-based zooming procedure, whose main feature is overcoming the need for zooming out at every switching instant, in order to compensate for the possible increment of the Lyapunov function at the switching instants. It is proven analytically that the resulting adjustments guarantee asymptotic state tracking. The proposed quantized adaptive control is applied to the piecewise linear model of the NASA Generic Transport Model aircraft linearized at multiple operating points.

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This paper addresses robust adaptive stabilization of uncertain switched time-delay systems with unknown disturbances in a high-order form. In addition to parametric uncertainty, an extra source of uncertainty arises from having time-varying delays. In particular, the upper bound of the changing rate of the delay is assumed to be unknown. To this purpose, a new reparametrization method is proposed, which incorporates both sources of uncertainty in a single scalar parameter. Therefore, a single scalar adaptive law is designed for parametric uncertainties and time-varying delays, which is combined with a new dynamic gain embedded in the control action. The new dynamic gain is designed to dominate the nonlinear effects caused by both the parametric uncertainty and the unknown variation of the time delay. The proposed design guarantees global asymptotic stability for arbitrary switching. A numerical example illustrates the effectiveness of the method.

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Managing grid-connected charging stations for fleets of electric vehicles leads to an optimal control problem where user preferences must be met with minimum energy costs (e.g., by exploiting lower electricity prices through the day, renewable energy production, and stored energy of parked vehicles). Instead of state-of-the-art charging scheduling based on open-loop strategies that explicitly depend on initial operating conditions, this paper proposes an approximate dynamic programming feedback-based optimization method with continuous state space and action space, where the feedback action guarantees
uniformity with respect to initial operating conditions, while price variations in the electricity and available solar energy are handled automatically in the optimization. The resulting control action is a multi-modal feedback, which is shown to handle a wide range of operating regimes, via a set of controllers whose action that can be activated or deactivated depending on availability
of solar energy and pricing model. Extensive simulations via a charging test case demonstrate the effectiveness of the approach.@en

In this paper, a novel Lyapunov function is proposed to study switched linear systems with a switching delay between activation of system modes and activation of candidate controller modes. The novelty consists in continuity of the Lyapunov function at the switching instants and discontinuity when the system modes and controller modes are matched. This structure is exploited to construct a time-varying Lyapunov function that is non-increasing at time instants of discontinuity. Stability criteria based on the novel Lyapunov function are developed to guarantee global asymptotic stability in the noiseless case. Most importantly, when exogenous disturbances are considered, the proposed Lyapunov function can be used to guarantee a finite non-weighted L₂ gain for asynchronously switched systems, for which Lyapunov functions proposed in literature are inconclusive. A numerical example illustrates the effectiveness of the proposed method.

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This work presents a distributed model reference adaptive methodology for output synchronization of heterogeneous linear agents with unknown dynamics. We consider a setting in which the control input is communicated among neighbors, instead of observer variables. For those agents that can access the signals of the reference model, classical model reference adaptation laws lead to leader synchronization; for those agents that cannot access such signals, synchronization must be achieved by taking the neighboring agents as an alternative reference model. We show that these two groups of agents give rise to two types of matching conditions: the standard conditions to match the reference model, and new distributed matching conditions among neighboring agents. Since all matching gains are unknown, the gains are adapted online via Lyapunov-based estimation. Asymptotic synchronization is proven analytically, and numerical examples show the effectiveness of the approach.

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This letter introduces a new switched adaptive control mechanism that can cope with parametric uncertainty while using discrete and saturated actuators. Control of air handling units (AHUs), where air and water supply have discrete and saturated characteristics, is the motivational drive behind this letter. We show that the cheap actuation and low computational requirements of building automation installations can be met after recasting the AHU thermal dynamics as a switched linear system with discrete working modes. Adaptive laws with anti-windup compensation and a switching law based on dwell time are introduced to cope with the uncertainties and input constraints of the switched linear system. Tracking performance is shown analytically and demonstrated via a numerical test case.

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The advances in distributed inter-vehicle communication networks have stimulated a fruitful line of research in Cooperative Adaptive Cruise Control (CACC). In CACC, individual vehicles, grouped into platoons, must automatically adjust their own speed using on-board sensors and communication with the preceding vehicle so as to maintain a safe inter-vehicle distance. However, a crucial limitation of CACC is that the string stability of the platoon can be proven only when the vehicles have identical driveline dynamics and perfect engine performance (homogeneous platoon), and possibly an ideal communication channel. This work proposes a novel CACC strategy that overcomes the homogeneity assumption and that is able to adapt its action and achieve string stability even for uncertain heterogeneous platoons. Moreover, in order to handle the inevitable communication losses, we formulate an extended average dwell-time framework and an adaptive switched control strategy which activates an augmented CACC or an augmented Adaptive Cruise Control strategy depending on communication reliability. Stability is proven analytically and simulations are conducted to validate the theoretical analysis.

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This paper investigates robust adaptive control of uncertain switched linear systems considering disturbances. Two modifications of the adaptive law of switched linear systems [1] based on parameter projection and a leakage approach are developed to guarantee the stability of the closed-loop switched
linear system: a projection law that requires knowledge of the bounds of the parameter estimates; and a leakage law based on initial conditions of the parameter estimates that does not require knowledge of the bounds of the parameter estimates. The closed-loop switched linear system is shown to be
globally uniformly ultimately bounded. In addition, the ultimate bounds of both adaptive control schemes are also given. A numerical example is provided to illustrate the effectiveness of the proposed methods.@en

In this paper, adaptive tracking control of switched nonlinear systems in the parametric strict-feedback form is investigated. After defining a reparametrisation lemma in the presence of a non-zero reference signal, we propose a new adaptive backstepping design of the virtual controllers that can handle the extra terms arising from the reparametrisation (and that the state-of-the-art backstepping designs cannot dominate). The proposed adaptive design guarantees, under arbitrarily fast switching, an a priori bound for the steady-state performance of the tracking error and a tunable bound for the transient error. Finally, the proposed method, by overcoming the need for subsystems with common sign of the input vector field, enlarges the class of uncertain switched nonlinear systems for which the adaptive tracking problem can be solved. A numerical example is provided to illustrate the proposed control scheme.

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This technical note establishes a novel result for adaptive asymptotic tracking control of uncertain switched linear systems. The result exploits a recently proposed stability condition for switched systems. In particular, a time-varying positive definite Lyapunov function is used to develop a novel piecewise continuous model-reference adaptive law and a dwell-time switching law. In contrast with previous research, where asymptotic tracking was possible only in the presence of a common Lyapunov function for the reference models, in this work asymptotic tracking is shown in a more general setting. Additionally, in the presence of persistence of excitation, the controller parameter estimation errors will converge to zero asymptotically. The main contribution of this work consists in establishing a symmetry between adaptive control of classical non-switched linear systems and adaptive control of switched linear systems. A practical example with an electro-hydraulic system is adopted to illustrate the results.@en

This paper investigates the problem of stabilizing switched linear systems with quantized output measurements. A technique to design a time-varying positive definite matrix is exploited to derive a novel Lyapunov function. A simplified
dynamic quantizer is proposed for switched linear systems based on the novel Lyapunov function with respect to state of the art. The adjustable coefficient μ influencing the accuracy of the dynamic quantizer increases during the zooming-out stage and decreases during the zooming-in stage, which is consistent with non-switched linear system. A numerical example is provided to illustrate the effectiveness of the proposed methods.@en

Grouping individual vehicles into platoons with a defined inter-vehicle spacing policy has been proven to greatly improve road throughput and reduce vehicles’ energy consumption. The emerging interest in distributed intervehicle
communication networks has provided new tools for further improvements of the performance of this platoon-based driving pattern. A leading control strategy of such vehicular cyber-physical systems is Cooperative Adaptive Cruise Control (CACC). However, a crucial limitation of the state-of-the-art is that string stability can be proven only when the vehicles in the platoon have identical driveline dynamics (homogeneous platoons). In this paper, we present a novel CACC strategy that overcomes the homogeneity assumption and that is able to adapt its action and achieve string stability even with uncertain
heterogeneous platoons. Considering a one-vehicle look-ahead topology, we propose a Model Reference Adaptive Control augmentation: the control objective is to augment a baseline CACC, proven to be string stable in the homogeneous scenario, with an adaptive control term that compensates for each vehicle’s unknown driveline dynamics. Asymptotic convergence of the heterogeneous platoon to a string stable platoon is shown analytically for an appropriately designed reference model.
Simulations of the proposed CACC strategy are conducted to validate the theoretical analysis.@en

Despite the progresses in Cooperative Adaptive Cruise Control (CACC), a crucial limitation of the state-of-the-art of this control scheme is that the string stability of the platoon can be proven only when the vehicles in the platoon have identical driveline dynamics (homogeneous platoons). In this paper, we present a novel control strategy that overcomes the homogeneity assumption and that is able to adapt its action and achieve string stability even with uncertain heterogeneous platoons with unknown engine performance losses and inevitable communication losses. Considering a one-vehicle look-ahead topology, we propose an adaptive switched control strategy: the control objective is to switch from an augmented CACC to an augmented Adaptive Cruise Control strategy when communication is lost based on a dwell time characterized switching law. The simulation of the proposed control strategy is conducted to validate the theoretical analysis.

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Estimation of energy models from data is an important part of advanced fault detection and diagnosis tools for smart energy purposes. Estimated energy models can be used for a large variety of management and control tasks, spanning from model predictive building control to estimation of energy consumption and user behavior. In practical implementation, problems to be considered are the fact that some measurements of relevance are missing and must be estimated, and the fact that other measurements, collected at low sampling rate to save memory, make discretization of physics-based models critical. These problems make classical estimation tools inadequate and call for appropriate dual estimation schemes where states and parameters of a system are estimated simultaneously. In this work we develop dual estimation schemes based on Extended Kalman Filtering (EKF) and Unscented Kalman Filtering (UKF) for constructing building energy models from data: in order to cope with the low sampling rate of data (with sampling time 15 min), an implicit discretization (Euler backward method) is adopted to discretize the continuous-time heat transfer dynamics. It is shown that explicit discretization methods like the Euler forward method, combined with 15 min sampling time, are ineffective for building reliable energy models (the discrete-time dynamics do not match the continuous-time ones): even explicit methods of higher order like the Runge–Kutta method fail to provide a good approximation of the continuous-time dynamics which such large sampling time. Either smaller time steps or alternative discretization methods are required. We verify that the implicit Euler backward method provides good approximation of the continuous-time dynamics and can be easily implemented for our dual estimation purposes. The applicability of the proposed method in terms of estimation of both states and parameters is demonstrated via simulations and using historical data from a real-life building.@en