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This paper formulates energy efficient driving of gasoline and electric powered vehicles as optimal control problems of various complexity. We show minimizing aerodynamic drag can maximize utilization of energy available at the wheel and requires low and constant speeds. By employing optimal control theory we show periods of maximal acceleration, maximal braking, and coasting often accompany constant speed cruising to satisfy boundary conditions on the states (bang-singular-bang optimal control). In the case of gasoline engine vehicles, analytical optimal control derivations show that pulse and glide operation of the engine while cruising can further reduce fuel use (chattering optimal control). For electric vehicles (EV), quadratic rather than linear dependence of energy use on control input results in different eco-driving patterns from gasoline engine vehicles. For EVs, analytical solution to the two point boundary value optimal control problem could be obtained after model simplification which is compared to numerical solution based on a more accurate model. We also evaluate optimal control solution in the presence of state constraints for EVs. Several simulation case studies are presented to showcase the energy efficiency gains with proposed eco driving strategies.

For discrete-time linear systems, we propose a suboptimal approach to constrained estimation so that the associated computation burden is reduced. This is achieved by enforcing a move blocking (MB) structure in the estimated process noise sequence (PNS). We show that full information estimation (FIE) and receding horizon estimation (RHE) with MB are both stable in the sense of an observer. The techniques in proving stability are inspired by those that have been proposed for standard RHE. To be specific, stability results are mainly achieved by (i) carefully embellishing the general assumptions for standard RHE to accommodate the MB requirement; (ii) exploiting the principle of optimality, as well as convexity of the quadratic programs (QPs) associated with FIE and RHE; (iii) relying on the fact that the Kalman filter is the best linear estimator in the least-squares sense. A crucial requirement in achieving stability for MB RHE is that the segment structure (SS) of the PNS of MB FIE for the optimization steps within the receding horizon (i.e., steps between T − N and T − 1 ) has to be enforced in the MB RHE optimization. As a result, the MB RHE strategy becomes a dynamic estimator with a periodically varying computational complexity. The theoretical results have been illustrated with examples.

In this note, novel linear matrix inequality (LMI) analysis conditions for the stability of linear parameter-varying (LPV) systems in input–output (IO) representation form are proposed together with bilinear matrix inequality (BMI) conditions for fixed-structure LPV-IO controller synthesis. Both the LPV-IO plant model and the controller are assumed to depend affinely and statically on the scheduling variables. By using an implicit representation of the plant and the controller interaction, an exact representation of the closed-loop behavior with affine dependence on the scheduling variables is achieved. This representation allows to apply Finsler’s Lemma for deriving exact stability as well as exact quadratic performance conditions. A DK-iteration based solution is carried out to synthesize the controller. The main results are illustrated by a numerical example.

We consider model predictive control (MPC) without terminal costs and constraints. Firstly, we rigorously show that MPC based on quadratic stage costs may fail, i.e., there does not exist a prediction horizon length such that a (controlled) equilibrium is asymptotically stable for the MPC closed loop although the system is, e.g., finite time controllable. Hence, stability properties of the infinite horizon optimal control problem are, in general, not preserved in MPC as long as purely quadratic costs are employed. This shows the necessity of using the stage cost as a design parameter to achieve asymptotic stability. Furthermore, we relax the standard controllability assumption employed in MPC without terminal costs and constraints to alleviate its verification.

We propose a central synergistic hybrid approach for global exponential stabilization on the Special Orthogonal group SO(3)SO(3). We introduce a new switching concept relying on a central family of (possibly) non-differentiable potential functions that enjoy the following properties: (1) being quadratic (as well as their gradients) with respect to the Euclidean attitude distance, and (2) being synergistic with respect to the gradient’s singular and/or critical points. The proposed approach is used to solve the attitude tracking problem, leading to global exponential stability results.

This work is concerned with asynchronous control for a class of two-dimensional switched systems with mode-dependent average dwell time. The systems are formulated by the famous Fornasini–Marchesini local state-space model, and the switching signal of the switched controller involves time delays which lead to the asynchronism between controllers and subsystems. By extending mode-dependent average dwell time with the switched quadratic Lyapunov functional approach, the stabilization condition is established for 2-D asynchronously switched systems. Based on the stabilization result, mode-dependent state-feedback controllers are designed to guarantee H ∞ performance and asymptotic stability of the corresponding closed-loop system. Finally, two examples are provided to illustrate the effectiveness of the proposed design scheme.

Input delay is an important type of actuator nonlinearity in control systems. In this paper, we will address the output-feedback control synthesis problem for linear systems with time-varying input delay under the integral quadratic constraint (IQC) framework. A new exact-memory control scheme is first proposed, which consists of a standard linear output-feedback control law and an internal delay loop. The delay loop is embedded in the controller structure so as to reproduce the input delay behavior of the plant. By using quadratic Lyapunov functions incorporated with dynamic IQC multipliers, the resulting dynamic output-feedback delay control synthesis problem is fully characterized by a set of linear matrix inequalities (LMIs), which are convex on all design variables including the scaling factors associated with the IQC multipliers. Moreover, the corresponding result on memoryless control is also derived for the case when the plant input-delay information is not available for feedback control. An application to network systems has been used to illustrate the effectiveness and usefulness of the proposed approach.

Sufficient conditions are presented for regional stability and nonlinear L2m gain analysis of linear systems subject to saturation, based on piecewise polynomial Lyapunov functions. The proposed conditions are formulated in terms of convex optimization problems and improve existing results both for the quadratic (L2 gain) and the polynomial (L2m gain) cases.

This paper describes a robust linear time-invariant output-feedback control strategy to reduce turbulent fluctuations, and therefore skin-friction drag, in wall-bounded turbulent fluid flows, that nonetheless gives performance guarantees in the nonlinear turbulent regime. The novel strategy is effective in reducing the supply of available energy to feed the turbulent fluctuations, expressed as reducing a bound on the supply rate to a quadratic storage function. The nonlinearity present in the equations that govern the dynamics of the flow is known to be passive and can be considered as a feedback forcing to the linearised dynamics (a Lur'e decomposition). Therefore, one is only required to control the linear dynamics in order to make the system close to passive. The ten most energy-producing spatial modes of a turbulent channel flow were identified. Passivity-based controllers were then generated to control these modes. The controllers require measurements of streamwise and spanwise wall-shear stress, and they actuate via wall transpiration. Nonlinear direct numerical simulations demonstrated that these controllers were capable of significantly reducing the turbulent energy and skin-friction drag of the flow.

Optimal robust MPC for constrained linear systems that are subject to additive uncertainty requires a closed loop optimization with computation that rises exponentially with the prediction horizon, N. This was overcome by parameterized tube MPC (PTMPC) that used a triangular separable prediction strategy in which predictions are decomposed into a nominal and N – 1 partial prediction sequences, each concerned with the compensation of a particular future disturbance. Beyond the first N steps, the PTMPC control law can be taken to be a static state feedback. Use of N – 1 partial prediction sequences causes the number of free variables and constraints to rise quadratically with N. To reduce this to linear, this paper proposes a modification of PTMPC that uses a single partial prediction sequence that is used in connection with all particular future disturbances but allows the compensatory effect of the partial prediction sequences to extend beyond the first N predictions. The prediction structure is of a triangular striped nature and extends over an infinite horizon. As illustrated by a simulation example, the resulting scheme can outperform PTMPC in terms of the size of the domain of attraction and affords a reduction in computation which allows for the use of longer horizon (for the same computational demand).

The stabilization problem of a class of nonlinear systems with actuator saturation is investigated via active disturbance rejection control (ADRC). We first present results for systems with nonlinear ADRC and show that local stabilization can be achieved in a region including the origin. Then, for the linear ADRC, the linear matrix inequality (LMI) conditions for determining the estimate of the domain of attraction of the resulting closed-loop system are formulated based on a quadratic candidate Lyapunov function and a generalized sector condition. An LMI-based algorithm is correspondingly established to design the linear ADRC controller. The obtained results suggest a new way to stabilize the saturated nonlinear system, even in the case that the state of the system is not fully available for measurement and system nonlinear dynamics are largely unknown. An illustrative example validates the effectiveness of the proposed approach.

In dynamic DNA nanotechnology, the DNA strand displacement technique provides the cornerstone for the bottom-up design of a man-made DNA molecular system. Practically, a feedback controller for regulating the concentration of a target DNA strand to the desired level is indispensable for mediating the kinetic momentum of a molecular actuator. However, such a regulator system operates by consuming fuel strands and requires sufficient supplies of these consumables for its normal execution, indicating that, in practice, optimal controller design requires the period of time during which the regulator proceeds with normal operation to be as long as possible. The fact that the system is naturally high dimensional and nonlinear complicates the analysis of properties emerging during a finite-time period in terms of their theoretical aspects. In this paper, we first define the new concept of a “finite-time regulation property” of DNA systems in the regulation problem. Then, to theoretically analyze this regulation property, we present two-time-scale modeling based on the difference in the initial distribution of the abundance of DNA strands. Focusing on the fast mode as a subsystem with a positive quadratic structure, we propose a new method for analyzing the regulation property observed in a finite period of time.

Constrained model predictive control (MPC) is a widely used control strategy, which employs moving horizon-based on-line optimisation to compute the optimum path of the manipulated variables. Nonlinear MPC can utilize detailed models but it is computationally expensive; on the other hand linear MPC may not be adequate. Piecewise affine (PWA) models can describe the underlying nonlinear dynamics more accurately, therefore they can provide a viable trade-off through their use in multi-model linear MPC configurations, which avoid integer programming. However, such schemes may introduce uncertainty affecting the closed loop stability. In this work, we propose an input to output stability analysis for closed loop systems, consisting of PWA models, where an observer and multi-model linear MPC are applied together, under unstructured uncertainty. Integral quadratic constraints (IQCs) are employed to assess the robustness of MPC under uncertainty. We create a model pool, by performing linearisation on selected transient points. All the possible uncertainties and nonlinearities (including the controller) can be introduced in the framework, assuming that they admit the appropriate IQCs, whilst the dissipation inequality can provide necessary conditions incorporating IQCs. We demonstrate the existence of static multipliers, which can reduce the conservatism of the stability analysis significantly. The proposed methodology is demonstrated through two engineering case studies., Comment: 28 pages 9 figures

This paper investigates the predictive control synthesis problem for constrained feedback control systems with both missing data and quantization. By introducing a missing data compensation strategy and an augmented Markov jump linear model with polytopic uncertainties, the effects of data loss and quantization on the system performance are considered simultaneously. A robust predictive control synthesis approach involving data missing and recovering probabilities is developed by minimizing an upper bound on the expected value of an infinite horizon quadratic performance objective at each sampling instant. Additional conditions to satisfy the input constraint in the presence of multiple missing data are also incorporated into the model predictive control (MPC) synthesis. Furthermore, both the recursive feasibility of the proposed MPC algorithm and the closed-loop mean-square stability are proved. Simulation results are given to illustrate the effectiveness of the proposed approach.

In the design of networked control systems, one must take account of communication constraints in the form of data rate. In this paper, we consider a quantized control problem for stabilizing uncertain linear systems in the sense of quadratic stability. For a class of finite-order (possibly time-varying) uncertain autoregressive plants, we show that the coarsest quantizer for achieving quadratic stabilization is of logarithmic type. In particular, for a given quadratic Lyapunov function, the largest coarseness is derived in an analytic form. The result explicitly shows that plants with more uncertainties require more precise information in the quantized signals to achieve quadratic stabilization. We also provide a numerical method based on a linear matrix inequality to search for a Lyapunov function along with a quantizer of a given level of coarseness.

In this paper, a necessary and sufficient condition for the exponential stability of linear systems with several time-delays is presented. Such a condition is based on the construction of quadratic lower bounds for the Lyapunov-Krasovskii functionals on the special Razumikhin-type set of functions. The result reveals a constructive procedure for the stability analysis whose application is illustrated with examples.

In this paper a previous approach, for the robust model predictive control (MPC) for a linear polytopic uncertain system, is extended to the case with bounded disturbance and unmeasurable state. The controller on-line optimizes a free control move followed by an output feedback control law based on the pre-specified state estimator. A key technique for this controller is an appropriate formulation of the estimation error bound which accounts for recursive feasibility of the optimization problem. The quadratic boundedness (QB) of the augmented state is guaranteed by the proposed approach. A numerical example is given to illustrate the effectiveness of the proposed controller.

This paper is concerned with the design of delta-sigma modulators via the generalized Kalman-Yakubovich-Popov lemma. The shaped noise transfer function (NTF) is assumed to have infinite impulse response, and the optimization objective is minimizing the maximum magnitude of the NTF over the signal frequency band. By virtue of the GKYP lemma, the optimization of an NTF is converted into a minimization problem subject to quadratic matrix inequalities, and then an iterative algorithm is proposed to solve this alternative minimization problem. Each iteration of the algorithm contains linear matrix inequality constraints only and can be effectively solved by the existing numerical software packages. Moreover, specifications on the NTF zeros are also integrated in the design method. A design example demonstrates that the proposed design method has an advantage over the benchmark one in improving the signal-to-noise ratio.

In this paper, a novel approach based on the Q -learning algorithm is proposed to solve the infinite-horizon linear quadratic tracker (LQT) for unknown discrete-time systems in a causal manner. It is assumed that the reference trajectory is generated by a linear command generator system. An augmented system composed of the original system and the command generator is constructed and it is shown that the value function for the LQT is quadratic in terms of the state of the augmented system. Using the quadratic structure of the value function, a Bellman equation and an augmented algebraic Riccati equation (ARE) for solving the LQT are derived. In contrast to the standard solution of the LQT, which requires the solution of an ARE and a noncausal difference equation simultaneously, in the proposed method the optimal control input is obtained by only solving an augmented ARE. A Q -learning algorithm is developed to solve online the augmented ARE without any knowledge about the system dynamics or the command generator. Convergence to the optimal solution is shown. A simulation example is used to verify the effectiveness of the proposed control scheme.

An adaptive output feedback tracking controller for nonholonomic mobile robots is proposed to guarantee that the tracking errors are confined to an arbitrarily small ball. The major difficulties are caused by simultaneous existence of nonholonomic constraints, unknown system parameters and a quadratic term of unmeasurable states in the mobile robot dynamic system as well as their couplings. To overcome these difficulties, we propose a new adaptive control scheme including designing a new adaptive state feedback controller and two high-gain observers to estimate the unknown linear and angular velocities respectively. It is shown that the closed loop adaptive system is stable and the tracking errors are guaranteed to be within the pre-specified bounds which can be arbitrarily small. Simulation results also verify the effectiveness of the proposed scheme.

Self-triggered control is a recently proposed paradigm that abandons the more traditional periodic time-triggered execution of control tasks with the objective of reducing the utilization of communication resources, while still guaranteeing desirable closed-loop behavior. In this paper, we introduce a self-triggered strategy based on performance levels described by a quadratic discounted cost. The classical LQR problem can be recovered as an important special case of the proposed self-triggered strategy. The self-triggered strategy proposed in this paper possesses three important features. Firstly, the control laws and triggering mechanisms are synthesized so that a priori chosen performance levels are guaranteed by design. Secondly, they realize significant reductions in the usage of communication resources. Thirdly, we address the co-design problem of jointly designing the feedback law and the triggering condition. By means of a numerical example, we show the effectiveness of the presented strategy. In particular, for the self-triggered LQR strategy, we show quantitatively that the proposed scheme can outperform conventional periodic time-triggered solutions. Keywords : Self-triggered control; Networked control systems; Linear quadratic regulator; Limiting control actions; LQG control

In this paper, a class of min-max optimal control problems with continuous dynamical systems and quadratic terminal constraints is studied. The main contribution is that the original terminal state constraint in which the disturbance is involved is transformed into an equivalent linear matrix inequality without disturbance under certain conditions. Then, the original min-max optimal control problem is solved via solving a sequence of semi-definite programming problems. An example is presented to illustrate the proposed method.

This paper is concerned with gain-scheduled control of two-dimensional discrete-time linear parameter-varying systems described by a Roesser state-space model with matrices depending affinely on time-varying scheduling parameters. The parameter admissible values and variations are assumed to belong to given intervals. Linear matrix inequality based methods are devised for designing static state feedback gain-scheduled controllers with either an H"~ or quadratic regulator-type performance. The control designs build on quadratically parameter-dependent Lyapunov functions and allow for incorporating information on available bounds on the parameters variation. The proposed controller gain can be independent, affine, quadratic, or a matrix fraction of quadratic polynomial matrices in the scheduling parameters.

To synthesize the optimal control strategies of nonlinear systems on infinite horizon while subject to mixed equality and inequality constraints has been a challenge to control engineers. This paper regards it as a problem of finite-time optimization in infinite-horizon control then devises a reinforcement learning agent, termed as the Adaptive Optimal Control (AOC) agent, to carry out the finite-time optimization procedures. Adaptive optimal control is in the sense of activating the finite-time optimization procedure whenever needed to improve the control strategy or adapt to a real-world environment. The Nonlinear Quadratic Regulator (NQR) is shown a typical example that the AOC agent can find out. The optimality conditions and adaptation rules for the AOC agent are deduced from Pontryagin's minimum principle. The requirements for convergence and stability of the AOC system are shown.

This paper investigates the problem of robust normalization and guaranteed cost control for descriptor systems with uncertainties. The parameter uncertainties are assumed to be time-varying norm-bounded appearing not only in both the state and input matrices but also in the derivative matrix. The quadratic performance index is nonstandard, which includes the additional derivative state term. Attention is focused on the proportional plus derivative state feedback controller design based on the linear matrix inequality method, which guarantees the closed-loop system to be normal and quadratically stable with a prescribed upper bound of the cost function.

This note considers the stability of linear systems with a time-varying delay. We are interested in a simple Lyapunov-Krasovskii functional (LKF) approach without delay decomposition. In this category, all recent tractable results had a fixed bound on the allowable maximum size of the delay for years. We propose a new simple LKF including the cross terms of variables and quadratic terms multiplied by a higher degree scalar function, and present a new result expressed in the form of LMIs. We show, by two well-known examples, that our result overcomes the previous allowable maximum size of delay and it is less conservative than the previous results having a relatively small upper bound in the derivative of time-delay.

In this paper, we present a new robust iterative learning control (ILC) design for a class of linear systems in the presence of time-varying parametric uncertainties and additive input/output disturbances. The system model is described by the Markov matrix as an affine function of parametric uncertainties. The robust ILC design is formulated as a min-max problem using a quadratic performance criterion subject to constraints of the control input update. Then, we propose a novel methodology to find a suboptimal solution of the min-max optimization problem. First, we derive an upper bound of the worst-case performance. As a result, the min-max problem is relaxed to become a minimization problem in the form of a quadratic program. Next, the robust ILC design is cast into a convex optimization over linear matrix inequalities (LMIs) which can be easily solved using off-the-shelf optimization solvers. The convergences of the control input and the error are proved. Finally, the robust ILC algorithm is applied to a physical model of a flexible link. The simulation results reveal the effectiveness of the proposed algorithm.

This paper studies linear time-invariant (LTI) control architectures for LTI plants when communication takes place over a scalar erasure channel. Assuming i.i.d. data dropouts, we first show that such a channel is equivalent, in a second order moment sense, to an additive white noise channel subject to an instantaneous signal-to-noise ratio constraint. This key result is then exploited in two ways: First, we use it to characterize the set of all LTI controllers that achieve mean square stability in control architectures closed over scalar erasure channels. Second, we use it to show that the optimal design of LTI controllers over scalar erasure channels can be carried out by using tools from standard quadratic optimal control theory. We finally apply our results to the dynamic output feedback control of LTI single-input single-output (SISO) plants subject to data dropouts. In this case, we are able to establish closed form necessary and sufficient conditions on the minimal successful transmission probability that allows one to design mean square stabilizing controllers.

This paper presents a new approach to constructive output feedback robust nonlinear controller design. The approach involves a class of controllers which include copies of the slope bounded nonlinearities occurring in the plant. Integral Quadratic Constraints and dynamic multipliers are introduced to exploit these repeated nonlinearities. The linear part of the controller is synthesized using minimax LQG control theory. This leads to a stabilizing nonlinear output feedback controller which gives an upper bound on the closed loop value of a quadratic cost functional.

This paper addresses the problem of stability analysis for a given class of nonlinear systems resulting from the connection of a linear system with an isolated backlash operator. Constructive conditions based on LMIs to ensure closed-loop stability are proposed by using some suitable Lyapunov functionals with quadratic terms and Lure type terms, and generalized sector conditions. Additionally, the boundary of the associated set of all the admissible equilibrium points is precisely defined.

This paper addresses the stabilization problem for single-input Markov jump linear systems via mode-dependent quantized state feedback. Given a measure of quantization coarseness, a mode-dependent logarithmic quantizer and a mode-dependent linear state feedback law can achieve optimal coarseness for mean square quadratic stabilization of a Markov jump linear system, similar to existing results for linear time-invariant systems. The sector bound approach is shown to be non-conservative in investigating the corresponding quantized state feedback problem, and then a method of optimal quantizer/controller design in terms of linear matrix inequalities is presented. Moreover, when the mode process is not observed by the controller and quantizer, a mode estimation algorithm obtained by maximizing a certain probability criterion is given. Finally, an application to networked control systems further demonstrates the usefulness of the results.

The stability and robustness of input-constrained model predictive control can be analyzed using the theory of integral quadratic constraints. We demonstrate the existence of improved multipliers when there are only staged input or box input constraints. This can significantly reduce the conservatism of any stability analysis, and we illustrate the improved performance with a simple numerical example.

This paper focuses on the delay-dependent robust H"~ filtering for uncertain discrete-time singular systems with interval time-varying delay. The uncertainty considered is a convex compact set of polytopic type. The purpose is the design of a linear robust H"~ filter such that the resulting filtering error singular system is regular, causal, and asymptotically stable with a H"~ norm bound. By establishing a finite sum inequality based on quadratic terms, a new delay-dependent bounded real lemma (BRL) for delayed singular systems is derived. Based on the derived BRL, a sufficient condition for the solvability of this problem is obtained in terms of linear matrix inequality (LMI) without decomposing the original system matrices. Also, it is shown that the proposed filter design method is general for both singular systems and non-singular systems. Finally, illustrative examples are presented to show the applicability of the proposed method.

By exploring some geometric properties of the logarithmic quantizer and using the fact that the logarithmic quantizer is sector bounded and nondecreasing, this paper presents a new approach to the stability analysis of quantized feedback control systems. Our method is based on Tsypkin-type Lyapunov functions that have been widely used in absolute stability analysis problems. The results are expressed in linear matrix inequalities (LMIs) and are valid for both single-input and multiple-input discrete-time linear systems with a logarithmic quantizer. Both theoretical analysis and numerical examples show that the results in this paper are generally less conservative than those in the quadratic framework.

The paper addresses the problem of analysis and static output feedback control synthesis for strict quadratic dissipativity of linear time-invariant systems with state-space symmetry. As a particular case of dissipative systems, we consider the mixed Hinfin and positive real performance criterion and we develop an explicit expression for calculating the Hinfin norm of these systems. Subsequently, an explicit parametrization of the static output feedback control gains that solve the mixed Hinfin and positive real performance problem is obtained. Computational examples demonstrate the use and computational advantages of the proposed explicit solutions.

This paper is concerned with stability of linear time-delay systems of both retarded and neutral types by using some new simple quadratic Lyapunov-Krasovskii functionals. These Lyapunov-Krasovskii functionals consist of two parts. One part comes from some existing Lyapunov-Krasovskii functionals employed in [Han, Q.-L. (2005a). Absolute stability of time-delay systems with sector-bounded nonlinearity. Automatica, 41, 2171-2176; Han, Q.-L. (2005b). A new delay-dependent stability criterion for linear neutral systems with norm-bounded uncertainties in all system matrices. International Journal of Systems Science, 36, 469-475]. The other part is constructed by uniformly dividing the discrete delay interval into multiple segments and choosing proper functionals with different weighted matrices corresponding to different segments. Then using these new simple quadratic Lyapunov-Krasovskii functionals, some new discrete delay-dependent stability criteria are derived for both retarded systems and neutral systems. It is shown that these criteria for retarded systems and neutral systems are always less conservative than the ones in Han (2005a) and Han (2005b) cited above, respectively. Numerical examples also show that the results obtained in this paper significantly improve the estimate of the discrete delay limit for stability over some other existing results.

This paper is concerned with the problem of parameter-dependent H"~ filtering for discrete-time systems with polytopic uncertainties. The uncertain parameters are supposed to reside in a polytope. Being different from previous results in the quadratic framework, the parameter-dependent Lyapunov function is used in this paper. Both full- and reduced-order filters are designed, which guarantee the asymptotic stability and a prescribed H"~ performance level. The filter parameters can be obtained from the solution of convex optimization problems in terms of linear matrix inequalities, which can be solved via efficient interior-point algorithms. Numerical examples are presented to illustrate the feasibility and less conservativeness of the proposed method.

We consider robust stability analysis of a class of large scale interconnected systems. The individual subsystems may be different but they are assumed to share a property that characterizes a set of interconnection matrices which lead to stable overall systems. The main contribution of the paper is to show that, for the case where the network interconnection matrix is normal, (robust) stability verification can be simplified to a low complexity problem of checking whether the frequency response of the individual subsystems and the eigenvalues of the interconnection matrix can be mutually separated using a class of quadratic forms. Most interestingly, it is shown that this criterion is also necessary, in the sense that if the criterion is violated, an interconnection matrix of the same eigenvalue distribution can be found to make the overall system unstable.

This paper introduces a new approach to robust adaptive H^~ control. The main idea of the paper is to extend an existing approach to robust H^~ control to allow for constant or slowly varying unknown parameters in an adaptive way. This is achieved by treating the presence of the unknown parameters as states resulting in a bilinear nonlinearity. A copy of this nonlinearity is repeated in the controller and the presence of the repeated nonlinearity is exploited using a special integral quadratic constraint.

In this paper stabilization of nonlinear systems with quadratic multi-input is considered. With the help of control Lyapunov function (CLF), a constructive parameterization of controls that globally asymptotically stabilize the system is proposed. Two different cases are considered. Firstly, under certain regularity assumptions, the feasible control set is parameterized, and continuous feedback stabilizing controls are designed. Then for the general case, piecewise continuous stabilizing controls are proposed. The design procedure can also be used to verify whether a candidate CLF is indeed a CLF. Several illustrative examples are presented as well.

This paper focuses on quadratic performance analysis and output feedback gain-scheduling synthesis for parameter-dependent systems with linear fractional representations (LFRs). New quadratic H"2 and L"2 performance analysis results based on full-block multipliers are given. A novel gain-scheduling output feedback synthesis, which can be regarded as a natural extension of the loop shaping design procedure of McFarlane and Glover to parameter-dependent systems, is proposed. This gain-scheduling technique is computationally attractive and yields a simple and transparent control structure that can be easily implemented. Its effectiveness is illustrated on a benchmark missile autopilot example.

This paper deals with quadratic stabilization of discrete-time multiple-input (MI) systems by means of quantized static feedback. We consider the minimization of quantization density, which is still an open problem for MI systems. Our first contribution in this regard is to partially derive the structure that a quantizer that minimizes density for an MI system should have. The second and main contribution of the paper is to develop a systematic design procedure for finite-density quadratically-stabilizing quantizers for MI systems. The resulting quantizers have a simple geometric structure and can be implemented via simple function evaluations. To the best of the authors' knowledge, no such design of finite-density quadratically-stabilizing quantizers has been previously proposed in the literature for general MI systems.

For robustness analysis with integral quadratic constraints, we formulate a new positivity condition on the solution of the corresponding linear matrix inequality which is necessary and sufficient for nominal stability of the underlying system. The application of this technical result is illustrated by a complete solution of the L"2-gain and robust H"2-estimator design problems if the uncertainties are characterized by dynamic integral quadratic constraints.

An optimal iterative learning control (ILC) is proposed to optimize an accumulative quadratic performance index in the iteration domain for the nominal dynamics of linear discrete-time systems. Properties of stability, convergence, robustness, and optimality are investigated and demonstrated. In the case that the system under consideration contains uncertain dynamics, the proposed ILC design can be applied to yield a guaranteed-cost ILC whose solution can be found using the linear matrix inequality (LMI) technique. Simulation examples are included to demonstrate feasibility and effectiveness of the proposed learning controls.

We derive conditions for quadratic stabilizability of linear networked control systems by dynamic output feedback and communication protocols. These conditions are used to develop a simultaneous design of controllers and protocols in terms of matrix inequalities. The obtained protocols do not require knowledge of controller and plant states but only of the discrepancies between current and the most recently transmitted values of nodes' signals, and are implementable on controller area networks. We demonstrate on a batch reactor example that our design guarantees quadratic stability with a significantly smaller network throughput than previously available designs.

Stability of systems in the presence of bounded uncertain time-varying delays in the feedback loop is studied. The delay parameter is assumed to be an unknown time-varying function for which the upper bounds on the magnitude and the variation are given. The stability problem is treated in the integral quadratic constraint (IQC) framework. Criteria for verifying robust stability are formulated as feasibility problems over a set of frequency-dependent linear matrix inequalities. The criteria can be equivalently formulated as semi-definite programs (SDP) using Kalman-Yakubovich-Popov lemma. As such, checking robust stability can be performed in a computationally efficient fashion.

International audience; Topological separation is investigated in the case of an uncertain time-invariant matrix interconnected with an implicit linear transformation. A quadratic separator independent of the uncertainty is shown to prove losslessly the closed-loop well-posedness. Several applications for LTI descriptor system analysis are then given. First, some known results for stability and pole location of descriptor systems are demonstrated in a new way. Second, contributions to robust stability analysis and time-delay systems stability analysis are exposed. These prove to be new even when compared to results for usual LTI systems (not in descriptor form). All results are formulated as linear matrix inequalities (LMIs).

In this paper, an explicit model predictive controller for the attitude of a satellite is designed. Explicit solutions to constrained linear MPC problems can be computed by solving multi-parametric quadratic programs (mpQP), where the parameters are the components of the state vector. The solution to the mpQP is a piecewise affine (PWA) function, which can be evaluated at each sample to obtain the optimal control law. The on-line computation effort is restricted to a table-lookup, and the controller can be implemented on inexpensive hardware as fixed-point arithmetics can be used. This is useful for systems with limited power and CPU resources. An example of such systems is micro-satellites, which is the focus of this paper. In particular, the explicit MPC (eMPC) approach is applied to the SSETI/ESEO micro-satellite, initiated by the European Space Agency (esa). The theoretical results are supported by simulations.

The integral-inequality method is a new way of tackling the delay-dependent stabilization problem for a linear system with time-varying state and input delays: [email protected]?(t)=Ax(t)+A"1x(t-h"1(t))+B"1u(t)+B"2u(t-h"2(t)). In this paper, a new integral inequality for quadratic terms is first established. Then, it is used to obtain a new state- and input-delay-dependent criterion that ensures the stability of the closed-loop system with a memoryless state feedback controller. Finally, some numerical examples are presented to demonstrate that control systems designed based on the criterion are effective, even though neither (A,B"1) nor (A+A"1,B"1) is stabilizable.

This paper considers actuator redundancy management for a class of overactuated nonlinear systems. Two tools for distributing the control effort among a redundant set of actuators are optimal control design and control allocation. In this paper, we investigate the relationship between these two design tools when the performance indexes are quadratic in the control input. We show that for a particular class of nonlinear systems, they give exactly the same design freedom in distributing the control effort among the actuators. Linear quadratic optimal control is contained as a special case. A benefit of using a separate control allocator is that actuator constraints can be considered, which is illustrated with a flight control example.