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Robust performance of control schemes for open quantum systems is investigated under classical uncertainties in the generators of the dynamics and nonclassical uncertainties due to decoherence and initial state preparation errors. A formalism is developed to measure performance based on the transmission of a dynamic perturbation or initial state preparation error to the quantum state error. This makes it possible to apply tools from classical robust control, such as structured singular value analysis. A difficulty arising from the singularity of the closed-loop Bloch equations for the quantum state is overcome by introducing the #-inversion lemma, a specialized version of the matrix inversion lemma. Under some conditions, this guarantees continuity of the structured singular value at $s = 0$. Additional difficulties occur when symmetry gives rise to multiple open-loop poles, which under symmetry-breaking unfold into single eigenvalues. The concepts are applied to systems subject to pure decoherence and a general dissipative system example of two qubits in a leaky cavity under laser driving fields and spontaneous emission. A nonclassical performance index, steady-state entanglement quantified by the concurrence, a nonlinear function of the system state, is introduced. Simulations confirm a conflict between entanglement, its log-sensitivity and stability margin under decoherence. [ABSTRACT FROM AUTHOR]

This article focuses on the problem of prescribed-time control for a class of uncertain nonlinear systems. First, a prescribed-time stability theorem is proposed by following the adaptive technology for the first time. Based on this theorem, a new state feedback control strategy is put forward by using the backstepping method for high-order nonlinear systems with unknown parameters to ensure the prescribed-time convergence. Moreover, the prescribed-time controller is obtained in the form of continuous time-varying feedback, which can render all system states converge to zero within the prescribed time. It should be noted that the prescribed time is independent of system initial conditions, which means that the prescribed time can be set arbitrarily within the physical limitations. Finally, two simulation examples are provided to illustrate the effectiveness of our proposed algorithm. [ABSTRACT FROM AUTHOR]

This article studies global robust output regulation of second-order nonlinear systems with input disturbances that encompass the fully-actuated Euler–Lagrange systems. We assume the availability of relative output (w.r.t. a family of reference signals) and output derivative measurements. Based on a specific separation principle and self-learning mechanism, we develop an internal model-based controller that does not require a priori knowledge of reference and disturbance signals and it only assumes that the kernels of these signals are a family of exosystems with unknown parameters (e.g., amplitudes, frequencies, or time periods). The proposed control framework has a self-learning mechanism that extricates itself from requiring absolute position measurement nor precise knowledge of the feedforward kernel signals. By requiring the high-level task/trajectory planner to use the same class of kernels in constraining the trajectories, the proposed low-level controller is able to learn the desired trajectories, to suppress the disturbance signals, and to adapt itself to the uncertain plant parameters. The framework enables a plug-and-play control mechanism in both levels of control. [ABSTRACT FROM AUTHOR]

This article addresses reconfiguration-based fault-tolerant control (FTC) with robust guaranteed performance for nonlinear uncertain systems under actuator faults. A PAssive/ACTive combined FTC method is proposed based on reliable control, which synthesizes the advantages of the active and passive FTC and strikes a balance between the performance and complexity of the method. Moreover, the reliability overcost of this method is reduced to balance the system nominal performance and reconfigurability. In this procedure, the $\theta$ -D method is used to solve the Hamilton–Jacobi–Bellman (HJB) and generalized HJB equations. Effectiveness of the proposed method is verified by a numerical example. [ABSTRACT FROM AUTHOR]

The Shapiro scheme, together with the closely related Frisch–Kalman scheme, has been an important approach to system identification and statistical analysis. A longstanding result on this scheme, known as the Shapiro theorem, is both informative and significant. This article imparts a geometric understanding to the Shapiro theorem and generalizes it to the asymmetric setting using the notion of cone-invariance. In particular, we establish the equivalence between two important properties of a real-valued square matrix—irreducible orthant-invariance and simplicity of its dominant eigenvalue under arbitrary diagonal perturbations. The result can be regarded as a converse Perron–Frobenius theorem. Furthermore, we investigate two applications of the proposed result in systems and control, namely, characterization of irreducibly orthant-monotone nonlinear systems and subspace tracking via decentralized control. We also extend the established result to accommodating polyhedral cones and obtain several insights. [ABSTRACT FROM AUTHOR]

This article aims to solve the problem of decentralized event-based finite-time control for a class of high-order interconnected nonlinear systems with an asymmetric output constraint. In order to achieve finite-time stability and reduce the update frequency of the controller, a novel controller and its event-trigger mechanism is proposed by adding a power integral technique and utilizing sign function. To fulfill the requirement of asymmetric output constraints, an asymmetric barrier Lyapunov function (BLF) is constructed, which is different from tan-type and log-type BLFs. Based on the contradictory idea and finite-time stability theory, it is proved that there is no Zeno phenomenon under this event-trigger mechanism and all state variables of the closed-loop system attenuate to the origin in the finite-time while the output signals never violate the constraint. Furthermore, the result in this article is expanded to fixed-time control. Finally, a simulation example is given to demonstrate the effectiveness of the presented strategy. [ABSTRACT FROM AUTHOR]

In this article, we aim at developing computationally tractable methods for nonlinear model/controller reduction. Recently, model reduction by generalized differential (GD) balancing has been proposed for nonlinear systems with constant input-vector fields and linear output functions. First, we study incremental properties in the GD balancing framework. Next, based on these analyses, we provide GD linear quadratic Gaussian (LQG) balancing and GD $H_\infty$ -balancing as controller reduction methods for nonlinear systems by focusing on linear feedback and observer gains. Especially for GD $H_\infty$ -balancing, we clarify when the closed-loop system consisting of the full-order system and a reduced-order controller is exponentially stable. All provided methods for controller reduction can be relaxed to linear matrix inequalities (LMIs). [ABSTRACT FROM AUTHOR]

For a family of genuinely nonlinear systems with delays in the input and state, global strong stabilization (GSS) in the sense of Kurzweil is shown to be possible by memoryless state and/or output feedback under two conditions: 1) The input delay is within an appropriate range although the state delays can be sufficiently large; 2) the time-delay bounding system is homogeneous of degree zero and has a lower triangular structure. The proof is based on the Lyapunov–Krasovskii functional theorem combined with the homogeneous domination philosophy. Using the emulation approach, we design memoryless homogeneous state and output feedback controllers, respectively, achieving GSS of the time-delay closed-loop systems with severe nonlinearity. Extensions to a wider class of time-delay nonlinear systems in the Hessenberg form are also given. Examples and counter-examples presented in this article illustrate not only the necessity of the homogeneous growth conditions but also the significance of the memoryless non-Lipschitz continuous feedback control strategies. [ABSTRACT FROM AUTHOR]

This article investigates the problem of how to control nonlinear systems with delays in the state by memoryless linear feedback. The notions of semiglobal asymptotic stabilization and sublevel sets are introduced in the context of time-delay systems. With the aid of Razumikhin theorem, we develop a semiglobal design method for the construction of Lyapunov functions, associated sublevel sets, and delay-free linear state feedback laws, step-by-step, achieving semiglobal asymptotic stabilization for time-delay nonlinear systems in a lower triangular form. In contrast to the global stabilization of nonlinear systems with delays in the state, which is usually achieved by dynamic state feedback (Lin and Zhang, 2020), the significance of this work is to point out that a tradeoff of the control objectives, e.g., semiglobal versus global stabilization, makes it possible to control a class of time-delay nonlinear systems by static linear feedback. Extensions to nonlinear systems with globally asymptotically locally expoentially stable (GALES)-like inverse dynamics are also included in this article. [ABSTRACT FROM AUTHOR]

Ensuring safety is crucial for the successful deployment of autonomous systems, such as self-driving vehicles, unmanned aerial vehicles, and robots acting close to humans. While there exist many controllers that optimize certain criteria, such as energy consumption, comfort, or low wear, they are usually not able to guarantee safety at all times for constrained nonlinear systems affected by disturbances. Many controllers providing safety guarantees, however, have no optimal performance. The idea of this article is, therefore, to synthesize a formally correct controller that serves as a safety net for an unverified, optimal controller. This way, most of the time, the optimal controller is in charge and leads to a desired, optimal control performance. The safety controller constantly monitors the actions of the optimal controller and takes over if the system would become unsafe. The safety controller utilizes a novel concept of backward reachable set computation, where we avoid the need of computing underapproximations of reachable sets. We have further developed a new approach that analytically describes reachable sets, making it possible to efficiently maximize the size of the backward reachable set. We demonstrate our approach by a numerical example from autonomous driving. [ABSTRACT FROM AUTHOR]

In this article we study integral-input-to-state stability (iISS) of nonlinear switched systems with jumps. We demonstrate by examples that iISS is not always preserved under slow enough dwell time switching, and then we present sufficient conditions for iISS to be preserved under slow switching. These conditions involve, besides a sufficiently large dwell time, some additional properties of comparison functions characterizing iISS of the individual modes. When the sufficient conditions that guarantee iISS are only partially satisfied, we are then able to conclude weaker variants of iISS, also introduced in this work. As an illustration, we show that switched systems with bilinear zero-input-stable modes are always iISS under sufficiently large dwell time. [ABSTRACT FROM AUTHOR]

Checking uniform attractivity of a time-varying dynamic system without a strict Lyapunov function is challenging as it requires the characterization of the limiting behavior of a set of trajectories. In the context of hybrid nonlinear time-varying systems, characterizing such limiting or convergent behaviors is even harder due to the complexity stemming from both continuous-time variations as well as discrete-time jumps. In this article, an extension of the standard hybrid time domain is introduced to define limiting behaviors, using set convergence, when time approaches either positive infinity or negative infinity. In particular, it is shown how to characterize limiting behaviors under the condition that an output signal approaches zero. Such limiting behaviors and their associated limiting systems can be used to verify uniform global attractivity. Particularly, a generalization of the classic Krasovskii–LaSalle theorem is obtained for hybrid time-varying systems. Two examples are used to demonstrate the effectiveness of the results. [ABSTRACT FROM AUTHOR]

We propose a state estimation methodology using a network of distributed observers. We consider a scenario in which the local measurement at each node may not guarantee the system's observability. In contrast, the ensemble of all the measurements does ensure that the observability property holds. As a result, we design a network of observers such that the estimated state vector computed by each observer converges to the system's state vector by using the local measurement and the communicated estimates of a subset of observers in its neighborhood. The proposed estimation scheme exploits sensor redundancy to provide robustness against faults in the sensors. Under suitable conditions on the redundant sensors, we show that it is possible to mitigate the effects of a class of sensor faults on the state estimation. Simulation trials demonstrate the effectiveness of the proposed distributed estimation scheme. [ABSTRACT FROM AUTHOR]

This article is devoted to the global continuous control for stochastic low-order cascade nonlinear systems with time-varying delay and stochastic inverse dynamics. Compared with existing results, the nature of only continuous, but nonsmooth, is unfolded since the power of the stochastic cascade system is of low order; and all the traditional growth conditions on unknown drift and diffusion nonlinearities and local Lipschitz condition are quitted, which largely extends the scope of application. Combining with stochastic input-to-state stability, two new lemmas are developed with rigorous proofs to deal with uncertain nonlinear terms and unmeasurable stochastic inverse dynamics. A continuous control scheme consisting of a delay-independent partial state feedback controller and a serial of dynamic update laws is proposed to guarantee the globally asymptotical stability of the closed-loop system. [ABSTRACT FROM AUTHOR]

In this article, the finite-time and fixed-time attractiveness problems are investigated for nonlinear impulsive systems. The aim of the proposed problems is to establish some general Lyapunov theorems and settling-time estimates for finite-time and fixed-time attractiveness of nonlinear impulsive systems by analysis technics. Moreover, some comparisons with the existing results are also given. The classical finite-time and fixed-time convergence theorems for nonlinear impulse-free systems are well extended to nonlinear impulsive systems by our results. Furthermore, the existing results of finite-time and fixed-time attractiveness for nonlinear impulsive systems are well improved. Finally, some simulations are utilized to illustrate the usefulness of the theoretical analysis. [ABSTRACT FROM AUTHOR]

In this article, we investigate a novel anytime control algorithm for wireless networked control with random dropouts. The controller computes sequences of tentative future control commands using time-varying (Markovian) computational resources. The sensor–controller and controller–actuator channel states are spatial- and time-correlated, respectively, and are modeled as a multistate Markov process. To compensate the effect of packet dropouts, a dual-buffer mechanism is proposed. We develop a novel cycle-cost-based approach to obtain the stability conditions on the nonlinear plant, controller, network, and computational resources. [ABSTRACT FROM AUTHOR]

The state-of-the-art quadratic-program-based control Lyapunov-barrier function (QP-CLBF) is a powerful control approach to balance safety and stability in an optimal fashion. However, under this approach, modeling inaccuracies may degrade the performance of closed-loop systems and cause violation or restriction of safety-critical constraints. This article presents an adaptive QP-CLBF approach for a class of nonlinear systems in the presence of parameter uncertainties with an unknown control coefficient. We begin by presenting a filtering-based concurrent learning (FCL) adaptive technique to guarantee simultaneous exponential convergence of system parameters and control coefficient. The proposed FCL extends and encompasses the baseline concurrent learning technique, which was developed to achieve exponential convergence of either system parameters exclusively or control coefficient while relying on the estimation of state derivatives using numerical smoothing. The proposed FCL adaptive method is then unified with a modified version of QP-CLBF to achieve exponential convergence of system parameters, control coefficient, and control Lyapunov and control barrier functions while establishing safety with the largest safe region. Under this unification, all results are exponential in the presence of modeling error without the need for numerical methods to estimate state derivatives. This is formally proven by employing a Lyapunov argument. Simulations are finally carried out to validate the theoretical results. [ABSTRACT FROM AUTHOR]

In this article, we study positive invariance and attractivity properties for nonlinear control systems, which are monotone with respect to proper cones. Monotonicity simplifies such analysis for specific sets defined by the proper cones. Instead of Lyapunov functions, a pair of so-called paths in the state space and input space play important roles. As applications, our results are utilized for analysis of asymptotic stability and also input-to-state stability on proper cones. The results are illustrated by means of examples. [ABSTRACT FROM AUTHOR]

This article proposes an adaptive second-order sliding mode (ASOSM) controller design by means of the Lyapunov method. The notable feature of the proposed algorithm is that it only needs boundedness of the uncertainties, whereas boundedness of the derivatives of uncertainties is not demanded. Under the proposed ASOSM control scheme, the gain can be dynamically tuned, which avoids gain overestimation. The finite-time stability of the closed-loop ASOSM dynamics is proved via the Lyapunov theory. Finally, the simulation results are shown to validate the theoretical analysis. [ABSTRACT FROM AUTHOR]

We consider the problem of identifying a dissipative linear model of an unknown nonlinear system that is known to be dissipative, from time-domain input–output data. We first learn an approximate linear model of the nonlinear system using standard system identification techniques and then perturb the system matrices of the linear model to enforce dissipativity, while closely approximating the dynamical behavior of the nonlinear system. Further, we provide an analytical relationship between the size of the perturbation and the radius in which the dissipativity of the linear model guarantees local dissipativity of the unknown nonlinear system. We demonstrate the application of this identification technique through two examples. [ABSTRACT FROM AUTHOR]

This article presents a time-invariant extremum seeking controller (ESC) for nonlinear autonomous systems with limit cycles. For this time-invariant ESC, we propose a method to prove the closed-loop system has an asymptotically stable limit cycle. The method is based on a perturbation theorem for maps, and, unlike existing techniques that use averaging and singular perturbation tools, it is not limited to weakly nonlinear systems. We use a typical example system to show that our method does indeed establish asymptotic stability of the limit cycle with minimal amplitude. Utilizing the example, we provide a general guide for analytic computations that are required to apply our method. The corresponding Mathematica code is available as supplementary material. [ABSTRACT FROM AUTHOR]

This article provides an extension of the observability rank condition to time-varying nonlinear systems. Previous conditions to check the state observability only hold for nonlinear systems that do not explicitly depend on time, or, for time-varying systems, they only account for the linear case. In this article, a general analytic condition is provided. The new condition reduces to the well-known observability rank condition in the two simpler cases of time-varying linear systems and time-invariant nonlinear systems. The proposed condition is applied to aerospace robotics to study the observability of a lunar-module-type system equipped with monocular vision and inertial sensors. [ABSTRACT FROM AUTHOR]

We examine the problem of testing a parametric form of the nonlinearity of Hammerstein systems against a nonparametric alternative. This article proposes test statistics relying on nonparametric orthogonal series regression function estimates. An asymptotic theory of the proposed tests is established including the asymptotic normality under the null hypothesis that the parametric form of the system nonlinearity is correct. Moreover, it is shown that under nonparametric alternatives, the probability of detecting that the parametric model is incorrect tends to one. The rate of detecting local alternatives is also established. [ABSTRACT FROM AUTHOR]

A novel method is proposed to ensure stability and constraint satisfaction, i.e., “compatibility,” for nonlinear affine systems. We require an asymptotically stabilizing control law and a zeroing control barrier function, and define a region of attraction for which the proposed control safely stabilizes the system. Our methodology requires checking conditions of the system dynamics over the state space, which may be computationally expensive. To facilitate the search for compatibility, we extend the results to a class of nonlinear systems, including mechanical systems, for which a novel controller is designed to guarantee passivity, safety, and stability. The proposed technique is demonstrated using numerical examples. [ABSTRACT FROM AUTHOR]

In this article, we develop a tracking model predictive control (MPC) scheme for nonlinear systems using the linearized dynamics at the current state as a prediction model. Under reasonable assumptions on the linearized dynamics, we prove that the proposed MPC scheme exponentially stabilizes the optimal reachable equilibrium w.r.t. a desired target setpoint. Our theoretical results rely on the fact that, close to the steady-state manifold, the prediction error of the linearization is small, and hence, we can slide along the steady-state manifold toward the optimal reachable equilibrium. The closed-loop stability properties mainly depend on a cost matrix, which allows us to trade off performance, robustness, and the size of the region of attraction. In an application to a nonlinear continuous stirred tank reactor, we show that the scheme, which only requires solving a convex quadratic program online, has comparable performance to a nonlinear MPC scheme while being computationally significantly more efficient. Furthermore, our results provide the basis for controlling nonlinear systems based on data-dependent linear prediction models, which we explore in our companion paper. [ABSTRACT FROM AUTHOR]

In this article, we present a novel data-driven model predictive control (MPC) approach to control unknown nonlinear systems using only measured input–output data with closed-loop stability guarantees. Our scheme relies on the data-driven system parameterization provided by the fundamental lemma of Willems et al. We use new input–output measurements online to update the data, exploiting local linear approximations of the underlying system. We prove that our MPC scheme, which only requires solving strictly convex quadratic programs online, ensures that the closed loop (practically) converges to the (unknown) optimal reachable equilibrium that tracks a desired output reference while satisfying polytopic input constraints. As intermediate results of independent interest, we extend the fundamental lemma to affine systems and we derive novel robustness bounds w.r.t. noisy data for the open-loop optimal control problem, which are directly transferable to other data-driven MPC schemes in the literature. The applicability of our approach is illustrated with a numerical application to a continuous stirred tank reactor. [ABSTRACT FROM AUTHOR]

This article investigates the transformation of Hamiltonian structures under sampling. It is shown that the exact sampled equivalent model associated to a given port-Hamiltonian continuous-time dynamics exhibits a discrete-time representation in terms of the discrete gradient, with the same energy function but modified damping and interconnection matrices. By construction, the proposed sampled-data dynamics guarantees exact matching of both the state evolutions and the energy-balance at all sampling instants. Its generalization to port-controlled Hamiltonian dynamics leads to characterize a new power conjugate output so recovering the concept of average passivation. On these bases, energy-management control strategies can be proposed. An energetic interpretation of the approach is confirmed by its formulation in the Dirac formalism. Two classical examples are worked out to validate the proposed sampled-data modeling in a comparative way with the literature. [ABSTRACT FROM AUTHOR]

This article is about the data-driven computation of optimal control for a class of control affine deterministic nonlinear systems. We assume that the control dynamical system model is not available, and the only information about the system dynamics is available in the form of time-series data. We provide a convex formulation for the optimal control problem (OCP) of the nonlinear system. The convex formulation relies on the duality result in the dynamical system’s stability theory involving density function and Perron–Frobenius operator. We formulate the OCP as an infinite-dimensional convex optimization program. The finite-dimensional approximation of the optimization problem relies on the recent advances made in the Koopman operator’s data-driven computation, which is dual to the Perron–Frobenius operator. Simulation results are presented to demonstrate the application of the developed framework. [ABSTRACT FROM AUTHOR]

Observability of nonlinear systems with unknown inputs was recently characterized in terms of dimension of an observability codistribution, obtained from Lie derivatives of outputs with respect to an infinite set of vector fields. However, the suggested stopping criterion does not apply to all systems, and the applicability condition is difficult to check. This article provides a new stopping criterion which holds universally and is easy to check. Moreover, we show that for systems with $n$ states, in the single-input single-output case the algorithm for computing observability codistribution converges in no more than $3n-1$ steps, while in the multi-input multi-output case addition of each independent input or output channel reduces this upper bound by one. [ABSTRACT FROM AUTHOR]

It is still an open problem to synthesize control with input and output quantizations for nonlinear systems subject to mismatched parametric uncertainties via backstepping design. This is because 1) the output becomes discontinuous and nondifferentiable after quantization, making the conventional recursive backstepping design method unsuitable as the differentiation of the virtual control signals does not exist, while the existing backstepping-based quantized control method is only applicable to systems modeled in normal form or systems without mismatched uncertainties; 2) it is difficult to deal with the impacts of errors caused by output quantization when the virtual control laws contain time-varying estimates of unknown parameters; and 3) since only the quantized output signal is available, the effects of certain items related to unknown parameters in currently available observers become difficult to be explicitly addressed. In this article, we present a solution to this problem by employing a dynamic filtering technique to avoid differentiating virtual control signals in backstepping design, using the parameter projection technique to design the parameter estimator and proposing a new form of state observer to facilitate the development of output feedback control. It is shown that, with the derived adaptive backstepping control involving both input and output quantizations, all the closed-loop signals are ensured bounded and the control performance in terms of the mean square error is adjustable through properly choosing certain design parameters. The benefits and effectiveness of the proposed scheme are also validated by numerical simulation. [ABSTRACT FROM AUTHOR]

This article provides finite-time stabilizing control laws for the continuous triangular systems, in which the nominal dynamics is the chain of power integrators with the power of a positive odd rational number. For a class of continuous lower-triangular systems, the linear controllers are designed. By invoking a vector Lyapunov function theory, there is no need to use the usual back-stepping technique and a quite number of inequality computations are avoided. For a class of continuous upper-triangular systems, the nested-saturation controllers are constructed. In this case, the use of a vector Lyapunov function theory also helps to reduce computational burden, and allows us to summarize a same group of parameter conditions guaranteeing both the reduction of saturated terms and the finite-time stability of the reduced system. [ABSTRACT FROM AUTHOR]

This work is concerned with a compositional technique for the construction of finite abstractions (a.k.a., finite Markov decision processes (MDPs)) for networks of discrete-time stochastic switched systems. We propose a framework based on a notion of stochastic simulation functions, using which one can quantify the probabilistic distance between original interconnected stochastic switched systems and their finite MDPs by leveraging dissipativity-type compositional conditions. We show that the proposed compositionality conditions can enjoy the structure of the interconnection topology and be potentially fulfilled independently of the number or gains of subsystems. We also propose an approach to construct finite MDPs together with their corresponding stochastic simulation functions for nonlinear stochastic switched systems satisfying some incremental passivity property. We show that for a particular class of nonlinear stochastic switched systems whose nonlinearities satisfy an incremental quadratic inequality, the aforementioned property can be readily checked by some linear matrix inequalities. To demonstrate the effectiveness of the proposed results, we apply our approaches to the following two different case studies: a road traffic network, and a fully interconnected network of nonlinear switched systems accepting different dissipativity properties. [ABSTRACT FROM AUTHOR]

In this article, we present a novel methodology to address the optimal output consensus problem for multiagent systems. We propose a distributed variable transformation that recasts the aforementioned problem into a simpler regulation problem of the new variables. The transformation requires only relative output measurements and is independent of any underlying agent dynamics and therefore applicable to a general class of systems. Classical control techniques, which take into account the agent dynamics and only need the relative outputs to be shared between neighbors, can then be employed to regulate the new variables. We utilize the methodology to address, for the first time, the problem of optimal output consensus for unknown pure-feedback agents with disturbances and state delays. Simulation studies on a group of continuous stirred tank reactors illustrate the validity of the theoretical analysis. [ABSTRACT FROM AUTHOR]

This article presents a new study on adaptive control of multi-input and multi-output (MIMO) discrete-time nonlinear systems with a noncanonical form involving parametric uncertainties. The adaptive control scheme employs a vector relative degree formulation to reconstruct the noncanonical system dynamics and derives a normal form. Then, a new matrix decomposition-based adaptive control scheme is proposed for the controlled plant with a vector relative degree $[1, 1,{\ldots }, 1]$ under some relaxed design conditions. In particular, the matrix decomposition technique is adopted to overcome the singularity problem during the adaptive estimation of an uncertain high-frequency gain matrix. The adaptive control scheme ensures closed-loop stability and asymptotic output tracking. An extension to the adaptive control of general canonical-form MIMO discrete-time nonlinear systems is also presented. Finally, through simulations, the effectiveness of the proposed control scheme is verified. [ABSTRACT FROM AUTHOR]

In this article, we propose a new approach to design globally convergent reduced-order observers for nonlinear control systems via contraction analysis and convex optimization. Despite the fact that contraction is a concept naturally suitable for state estimation, the existing solutions are either local or relatively conservative when applying to physical systems. To address this, we show that this problem can be translated into an offline search for a coordinate transformation after which the dynamics is (transversely) contracting. The obtained sufficient condition consists of some easily verifiable differential inequalities, which, on one hand, identify a very general class of “detectable” nonlinear systems, and on the other hand, can be expressed as computationally efficient convex optimization, making the design procedure more systematic. Connections with some well-established approaches and concepts are also clarified in this article. Finally, we illustrate the proposed method with several numerical and physical examples, including polynomial, mechanical, electromechanical, and biochemical systems. [ABSTRACT FROM AUTHOR]

Dissipativity properties have proven to be very valuable for systems analysis and controller design. With the rising amount of available data, there has, therefore, been an increasing interest in determining dissipativity properties from (measured) trajectories directly, while an explicit model of the system remains undisclosed. Most existing approaches for data-driven dissipativity, however, guarantee the dissipativity condition only over a finite-time horizon and provide weak or no guarantees on robustness in the presence of noise. In this article, we present a framework for verifying dissipativity properties from measured data with desirable guarantees. We first consider the case of input-state measurements, where we provide computationally attractive conditions in the presence of process noise. We extend this approach to input–output data, where similar results hold in the noise-free case, and finally provide results for the case of noisy input–output trajectories. [ABSTRACT FROM AUTHOR]

Although rich collection of research results on event-triggered control exist, no effort has ever been made in integrating state/output triggering and controller triggering simultaneously with backstepping control design. The primary objective of this article is, by using intermittent output signal only, to build a backstepping adaptive event-triggered feedback control for a class of uncertain nonlinear systems. To do so, we need to tackle three technical obstacles. First, the nature of the event triggering makes the transmitted output signal discontinuous, rendering the regular recursive backstepping design method inapplicable as the repetitive differentiation of virtual control signals is literally undefined. Second, the effects arisen from the event-triggering action must be properly accommodated, but the current compensating method only works for systems in normal form, thus a new method needs to be developed in order to handle nonnormal form systems. Third, as only intermittent output signal is available, and at the same time, the impacts of certain terms containing unknown parameters (arising from event triggering) need to be compensated, it is rather challenging to design a suitable state observer. To circumvent these difficulties, we employ the dynamic filtering technique to avoid the differentiation of virtual control signals in the backstepping design, construct a new compensation scheme to deal with the effects of output triggering, and build a new form of state observer to facilitate the development of output feedback control. It is shown that, with the derived adaptive backstepping output-triggered control, all the closed-loop signals are ensured bounded and the transient system performance in the mean square error sense can be adjusted by appropriately adjusting design parameters. The benefits and effectiveness of the proposed scheme are also validated by numerical simulation. [ABSTRACT FROM AUTHOR]

In a recent article, we have shown how to learn controllers for unknown linear systems using finite-length noisy data by solving linear matrix inequalities. In this article, we extend this approach to deal with unknown nonlinear polynomial systems by formulating stability certificates in the form of data-dependent sum of squares programs, whose solution directly provides a stabilizing controller and a Lyapunov function. We then derive variations of this result that lead to more advantageous controller designs. The results also reveal connections to the problem of designing a controller starting from a least-square estimate of the polynomial system. [ABSTRACT FROM AUTHOR]

A linear dynamical system is called $k$ -positive if its dynamics maps the set of vectors with up to $k-1$ sign variations to itself. For $k=1$ , this reduces to the important class of positive linear systems. Since stable positive linear time-invariant systems always admit a diagonal quadratic Lyapunov function, i.e., they are diagonally stable, we may expect that this holds also for stable $k$ -positive systems. We show that, in general, this is not the case both in the continuous-time and discrete-time (DT) case. We then focus on DT $k$ -positive linear systems and introduce the new notion of the DT $k$ -diagonal stability. It is shown that this is a necessary condition for the standard DT diagonal stability. We demonstrate an application of this new notion to the analysis of a class of DT nonlinear systems. [ABSTRACT FROM AUTHOR]

This technical article investigates the problem of event-triggered gain-scheduling control of nonlinear systems. The considered class of nonlinear systems is such that an equivalent local polytopic model is obtained. By following the codesign approach, it is performed the simultaneous design of the dynamic event-triggering mechanism (ETM) and the gain-scheduled controller parameterized in terms of state-dependent scheduling functions. As the state information is only available to the controller at specific instants determined by the ETM, the scheduling functions of controller and plant polytopic model are asynchronous. To cope with this drawback, the trigger function of the dynamic ETM is appropriately defined to mitigate the influence of asynchronous scheduling functions in the Lyapunov stability-based analysis, allowing to derive a less conservative codesign condition. A convex optimization problem with linear matrix inequality constraints is proposed to perform the codesign and to enlarge the interevent times. Also, it is shown that there exists a lower bound for the interevent times, which prevents Zeno behavior. Numerical examples are provided to illustrate the advantages of the proposed dynamic event-triggered control codesign approach over emulation-based approach and its static counterpart. [ABSTRACT FROM AUTHOR]

Numerous state-feedback and observer designs for nonlinear dynamic systems (NDS) have been developed in the past three decades. These designs assume that NDS nonlinearities satisfy one of the following function set classifications: bounded Jacobian, Lipschitz continuity, one-sided Lipschitz, quadratic inner-boundedness, and quadratic boundedness. These function sets are characterized by constant scalars or matrices bounding the NDS’ nonlinearities. These constants depend on the NDS’ operating region, topology, and parameters and are utilized to synthesize observer/controller gains. Unfortunately, there is a near-complete absence of algorithms to compute such bounding constants. In this article, we develop analytical and computational methods to compute such constants. First, for every function set classification, we derive analytical expressions for these bounding constants through global maximization formulations. Second, we utilize a derivative-free interval-based global maximization algorithm based on the branch-and-bound framework to numerically obtain the bounding constants. Third, we showcase the effectiveness of our approaches to compute the corresponding parameters on some NDS such as highway traffic networks and synchronous generator models. [ABSTRACT FROM AUTHOR]

This article addresses the observability analysis and the optimal design of observation parameters in the presence of noisy measurements and parametric uncertainties. The notion of almost $\epsilon$ -observability is introduced and a systematic procedure to assess its satisfaction for a given system with a priori known measurement noise statistics and parameter discrepancy is sketched. Moreover, the concept of observation-target quantities is introduced to analyze the precision with which specific chosen expressions of the state and the parameters can be reconstructed. The overall framework is exposed and validated through an illustrative example. [ABSTRACT FROM AUTHOR]

We consider optimal control problems for continuous-time systems with time-dependent dynamics, in which the time-dependence arises from the presence of a known exogenous signal. The problem has been elegantly solved in the case of linear input-affine systems, for which it has been shown that the solution has a remarkable structure: It is given by the sum of two contributions; a state feedback, which coincides with the unperturbed optimal control law, and a purely feedforward term in charge of compensating the effect of the exogenous signal. The objective of this article is to extend the above result to nonlinear input-affine systems. It is shown that, while some of the relevant features of the linear case indeed rely heavily on linearity and are not preserved in the nonlinear setting, several structural claims can be proved also in the nonlinear case. [ABSTRACT FROM AUTHOR]

In this article, the output feedback-based direct model reference adaptive control of piecewise affine systems and its parameter convergence are investigated. Under the slow switching assumption, it is shown that all the closed-loop signals are bounded and the output tracking error is small in the mean square sense. Built upon this result, the estimation error of controller parameters is proved to converge to a residual set if the input signal is sufficiently rich. The relationship between the size of this residual set and the switching frequency is established. Moreover, the convergence of the estimated controller parameters to their nominal values can be achieved for a certain subsystem given that this subsystem is activated for infinitely long time. Simulation results validate the effectiveness of the proposed approach. [ABSTRACT FROM AUTHOR]

This article addresses the problem of learning the optimal control policy for a nonlinear stochastic dynamical. This problem is subject to the “curse of dimensionality” associated with the dynamic programming method. This article proposes a novel decoupled data-based control (D2C) algorithm that addresses this problem using a decoupled, “open-loop–closed-loop,” approach. First, an open-loop deterministic trajectory optimization problem is solved using a black-box simulation model of the dynamical system. Then, closed-loop control is developed around this open-loop trajectory by linearization of the dynamics about this nominal trajectory. By virtue of linearization, a linear quadratic regulator based algorithm can be used for this closed-loop control. We show that the performance of D2C algorithm is approximately optimal. Moreover, simulation performance suggests a significant reduction in training time compared to other state-of-the-art algorithms. [ABSTRACT FROM AUTHOR]