Publications
238 results found
Angeli D, Nešić D, 2001, Power characterizations of input-to-state stability and integral input-to-state stability, IEEE Transactions on Automatic Control, Vol: 46, Pages: 1298-1303, ISSN: 0018-9286
New notions of external stability for nonlinear systems are introduced, making use of average powers as signal norms and comparison functions as in the input-to-state stability (ISS) framework. Several new characterizations of ISS and integral ISS are presented in terms of the new notions. An example is discussed to illustrate differences and similarities of the newly introduced properties.
Angeli D, 2001, Almost global stabilization of the inverted pendulum via continuous state feedback, Automatica, Vol: 37, Pages: 1103-1108, ISSN: 0005-1098
Continuous state feedback laws are presented for "almost" global stabilization of the planar inverted pendulum on a cart. The synthesis is carried out exploiting energy-shaping techniques and a suitable smooth switching between positive and negative feedback. Some of the employed ideas could be possibly generalized to the problem of stabilization of systems with multiple equilibrium points. © 2001 Elsevier Science Ltd.
Angeli D, Casavola A, Mosca E, 2001, Predictive control with partial state information, Pages: 962-967
A method is described in order to address control problems in the presence of state and input constraints for noisy linear plants under partial state information. The approach consists in reducing the problem to a full-state feedback strategy for an auxiliary system subject to suitably modified constraints and disturbances. This is particularly useful in the context of model predictive control since traditional MPC schemes usually require exact knowledge of the state. Moreover, the overall procedure leads to MPC schemes based on closed-loop predictions and hence less affected by conservativeness. As an example of application we discuss the implementation of a predictive controller for a two-carts/spring system under input constraints and bounded persistent disturbances.
Angeli D, Casavola A, Mosca E, 2001, Global regulation of input-saturated discrete-time linear systems subject to persistent disturbances, Pages: 3207-3212
Two control strategies are described and contrasted for globally stabilizing ANCBI linear plants subject to input constraints in the presence of persistent, arbitrarily large but bounded, disturbances. The first technique is based on a weaker concept of robust positive invariance, referred to in the paper as positive quasi d-invariance. The second method is based on the classic concept of positive d-invariance.
Angeli D, Nešić D, 2001, Power formulations of input to state stability notions, Proceedings of the IEEE Conference on Decision and Control, Vol: 1, Pages: 893-898, ISSN: 0191-2216
The characterizations of input-to-state stability (ISS) and integral input-to-state stability were presented. The characterizations were given in terms of powers of input and/or state signals and were novel compared to previous characterizations. The results showed that ISS systems possessed the property that bounded energy inputs implied bounded energy states.
Angeli D, Ingalls B, Sontag ED, et al., 2001, Asymptotic characterizations of IOSS, Proceedings of the IEEE Conference on Decision and Control, Vol: 1, Pages: 881-886, ISSN: 0191-2216
We present new characterizations of input-output-to-state stability This is a notion of detectability formulated in the ISS framework. Equivalent properties are presented in terms of asymptotic estimates of the state variables on the basis of external information provided by input and output signals. Such results, when applied to other stability notions such as integral ISS and DISS, provide equivalent characterizations involving asymptotic gains for the corresponding stability notions as well.
Angeli D, Nešić D, 2001, A trajectory based approach for stability robustness of systems with inputs, Proceedings of the IEEE Conference on Decision and Control, Vol: 1, Pages: 485-490, ISSN: 0191-2216
We show, for a definition of semiglobal practical external stability, that the stability property holds on semi-infinite time intervals if and only if it holds on arbitrarily long but finite time intervals. These results have immediate applications in analysis of stability properties of highly oscillatory systems with inputs using averaging or for systems with inputs that are slowly varying. Results are stated for general flows and the stability is given with respect to arbitrary (not necessarily compact) sets.
Arcak M, Angeli D, Sontag E, 2001, Stabilization of cascades using integral input-to-state stability, Proceedings of the IEEE Conference on Decision and Control, Vol: 4, Pages: 3814-3819, ISSN: 0191-2216
We analyze nonlinear cascades in which the driven subsystem is integral ISS, and characterize the admissible integral ISS gains for stability. This characterization makes use of the convergence speed of the driving subsystem, and allows a larger class of gain functions when the convergence is faster. We show that our integral ISS gain characterization unifies different approaches in the literature which restrict the nonlinear growth of the driven subsystem and the convergence speed of the driving subsystem.
Angeli D, Mosca E, 2001, Lyapunov-based switching supervisory control of nonlinear uncertain systems, Pages: 967-972, ISSN: 0743-1619
The problem of controlling nonlinear noisy systems affected by parametric uncertainties is approached via the introduction of a supervisor which switches on, in feedback to the plant, one controller selected from a finite set of predesigned controllers. A Lyapunov-based falsification criterion allows one to ensure robust stability in the presence of uncertain constant parameters and exogenous bounded disturbances.
Angeli D, Casavola A, Mosca E, 2001, On feasible set-membership state estimators in constrained command governor control, Automatica, Vol: 37, Pages: 151-156, ISSN: 0005-1098
An analysis is presented on the feasibility issue in command governor (CG) control with deterministic set-membership state estimators for determining the state uncertainty set (SUS), viz. the set of all states which are compatible with measurements and a priori knowledge on the system. It is shown that the recipe of modifying standard receding horizon CG schemes based on the full knowledge of the state is effective provided that the latter is exactly computed at any time. On the contrary, when simple-shaped outer approximations of SUS are exploited for reducing the numerical complexity of the algorithm, loss of solvability or stability may result.
Angeli D, 2000, A Lyapunov approach to incremental stability, Pages: 2947-2952, ISSN: 0191-2216
This paper deals with several notions of incremental stability. In other words, we focus on stability of trajectories with respect to one another, rather than with respect some attractor or equilibrium point. The aim is to present a framework for understanding such questions fully compatible with the well-known Input-to-State Stability approach.
Casavola A, Mosca E, Angeli D, 2000, Robust command governors for constrained linear systems, IEEE Transactions on Automatic Control, Vol: 45, Pages: 2071-2077, ISSN: 0018-9286
Robust command governors are designed for discrete-time linear time-variant (LTV) system with polytopic uncertainty models and subject to unknown bounded disturbances and pointwise-in-time input and state-related constraints.
Angeli D, Casavola A, Mosca E, 2000, Constrained predictive control of nonlinear plants via polytopic linear system embedding, International Journal of Robust and Nonlinear Control, Vol: 10, Pages: 1091-1103, ISSN: 1049-8923
This paper considers nonlinear system control via robust predictive controllers developed for constrained LTV systems with polytopic model uncertainties. The nonlinear systems dealt with are the ones whose trajectories can be embedded within those of a polytopic LTV system. This condition can be satisfied in bounded regions of the state space for a large class of nonlinear systems. In particular, we focus our attention on a robust predictive control scheme similar to the one recently developed by two of the authors for input-saturated polytopic LTV discrete-time systems, here extended so as to take into account also state constraints. The solution is based on the minimization, at each time instant, of an upper bound of the 'worst-case' infinite horizon quadratic cost under the constraint of steering the convex hull of the predicted state set into a feasible and robust positive invariant region. A condition on the initial state is given that suffices to ensure problem solvability for all subsequent time instants. The proposed predictive controller is proved to robustly quadratically stabilize input and state-constrained LTV polytopic systems, as well as any other embedded nonlinear system.
Angeli D, Sontag ED, Wang Y, 2000, Further equivalences and semiglobal versions of integral input to state stability, Dynamics and Control, Vol: 10, Pages: 127-149, ISSN: 0925-4668
This paper continues the study of the integral input-to-state stability (IISS) property. It is shown that the IISS property is equivalent to one which arises from the consideration of mixed norms on states and inputs, as well as to the superposition of a 'bounded energy bounded state' requirement and the global asymptotic stability of the unforced system. A semiglobal version of IISS is shown to imply the global version, though a counterexample shows that the analogous fact fails for input to state stability (ISS). The results in this note complete the basic theoretical picture regarding IISS and ISS.
Angeli D, Sontag ED, Wang Y, 2000, A characterization of integral input-to-state stability, IEEE Transactions on Automatic Control, Vol: 45, Pages: 1082-1097, ISSN: 0018-9286
The notion of input-to-state stability (ISS) is now recognized as a central concept in nonlinear systems analysis. It provides a nonlinear generalization of finite gains with respect to supremum norms and also of finite L2 gains. It plays a central role in recursive design, coprime factorizations, controllers for nonminimum phase systems, and many other areas. In this paper, a newer notion, that of integral input-to-state stability (iISS), is studied. The notion of iISS generalizes the concept of finite gain when using an integral norm on inputs but supremum norms of states, in that sense generalizing the linear "H2" theory. It allows one to quantify sensitivity even in the presence of certain forms of nonlinear resonance. We obtain here several necessary and sufficient characterizations of the iISS property, expressed in terms of dissipation inequalities and other alternative and nontrivial characterizations. These characterizations serve to show that integral input-to-state stability is a most natural concept, one that might eventually play a role at least comparable to, if not even more important than, ISS. © 2000 IEEE.
Angeli D, Casavola A, Mosca E, 2000, Predictive PI-control of linear plants under positional and incremental input saturations, Automatica, Vol: 36, Pages: 1505-1516, ISSN: 0005-1098
A predictive control strategy is developed for set-point tracking of LTI plants in the presence of joint positional and incremental (rate) input saturation constraints. The resulting control algorithm is built so as to provide an integral action capable to asymptotically reject arbitrary constant disturbances. This task is achieved by possibly modifying on-line the set-point in the case this becomes incompatible with constraints and disturbances. When applied to asymptotically null controllable with bounded inputs (ANCBI) plants, viz. all stabilizable linear systems with eigenvalues in the closed unit circle, the control law is shown to globally provide set-point tracking in the presence of arbitrary constant disturbances and initial state. For non-ANCBI plants, viz. systems with exponentially unstable modes, the control law features the mentioned properties locally, viz. in bounded regions of initial states and disturbances. © 2000 Elsevier Science Ltd. All rights reserved.
Angeli D, Mosca E, Casavola A, 2000, Output predictive control of linear plants with saturated and rate limited actuators, Pages: 272-276, ISSN: 0743-1619
A predictive control strategy is presented for set-point tracking and global stabilization of ANCBI plants in the presence of actuators with position and rate saturation constraints and without full state accessibility. It is shown that the same properties achievable in the case of full state availability can be recovered by using a deadbeat observer.
Angeli D, Sontag ED, 1999, Forward completeness, unboundedness observability, and their Lyapunov characterizations, Systems and Control Letters, Vol: 38, Pages: 209-217, ISSN: 0167-6911
A finite-dimensional continuous-time system is forward complete if solutions exist globally, for positive time. This paper shows that forward completeness can be characterized in a necessary and sufficient manner by means of smooth scalar growth inequalities. Moreover, a version of this fact is also proved for systems with inputs, and a generalization is also provided for systems with outputs and a notion (unboundedness observability) of relative completeness. We apply these results to obtain a bound on reachable states in terms of energy-like estimates of inputs. © 1999 Elsevier Science B.V. All rights reserved.
Angeli D, 1999, Intrinsic robustness of global asymptotic stability, Systems and Control Letters, Vol: 38, Pages: 297-307, ISSN: 0167-6911
Equivalence is shown for discrete time systems between global asymptotic stability and the so-called integral Input-to-State Stability. The latter is a notion of robust stability with respect to exogenous disturbances which informally translates into the statement "no matter what is the initial condition, if the energy of the inputs is small, then the state must eventually be small". © 1999 Elsevier Science B.V. All rights reserved.
Angeli D, Sontag ED, 1999, Characterizations of forward completeness, Pages: 2551-2556, ISSN: 0191-2216
A finite-dimensional continuous-time system is forward complete if solutions exist globally, for positive time. This paper shows that forward completeness can be characterized in a necessary and sufficient manner by means of smooth scalar growth inequalities. Moreover, a version of this fact is also proved for systems with inputs, and a generalization is also provided for systems with outputs and a notion (unboundedness observability) of relative completeness. We apply these results to obtain a bound on reachable states in terms of energy-like estimates of inputs.
Angeli D, 1999, Input-to-state stability of PD-controlled robotic systems, Automatica, Vol: 35, Pages: 1285-1290, ISSN: 0005-1098
The external stability for nonlinear systems is investigated. An important issue in systems theory is to provide suitable estimates of these state variables in terms of past inputs. A sufficient condition for input-to-state stability is presented for systems admitting a Lyapunov function with negative semi-definite derivative. An application to proportional-derivative-controlled robotic manipulators is described.
Angeli D, Mosca E, 1999, Command governors for constrained nonlinear systems, IEEE Transactions on Automatic Control, Vol: 44, Pages: 816-820, ISSN: 0018-9286
A method is described for set-point tracking in nonlinear systems when pointwise-in-time input and/or state inequality constraints are to be enforced. It consists of adding to a primal compensated system a nonlinear device called command governor (CG) whose action is based on the current state, set-point, and prescribed constraints. The CG selects at any time the system input via a receding-horizon strategy from a virtual sequence amongst all possible command sequences by solving a constrained quadratic optimization problem. Provided that the initial state be admissible, the overall system is proved to fulfill the constraints and have desirable performance stability properties.
Angeli D, Casavola A, Mosca E, 1999, Command governors for constrained nonlinear systems: Direct nonlinear vs. linearization-based strategies, International Journal of Robust and Nonlinear Control, Vol: 9, Pages: 677-699, ISSN: 1049-8923
Two command governors (CG) are described for solving set-point tracking problems for nonlinear systems when pointwise-in-time input and/or state related inequality constraints have to be fulfilled. A CG is a nonlinear device which is added to a primal compensated system. The CG action, based on the current state, set-point and prescribed constraints, is finalized to select, at any time, a command sequence under which the constraints are possibly fulfilled with acceptable tracking performance. The two CGs, both based on the receding horizon control philosophy, differ in that one directly exploits the nonlinear model of the primal system, whereas the other is based on the property that, under some conditions, all trajectories of a nonlinear system are embedded within the trajectories of a linear time-varying (LTV) uncertain system. An example is presented so as to exhibit the relative merits of the methods.
Angeli D, Casavola A, Giannelli M, et al., 1998, Switching supervisory predictive control of input saturated plants, Pages: 1155-1159
A predictive control scheme based on a blend of receding-horizon plus switching-control ideas is presented for regulating linear plants subject to input saturation constraints. While only local asymptotic regulation can be ensured in general, semiglobal exponential regulation is achieved for linear plants which are free of exponentially unstable modes. The overall scheme is based on a fixed finite set of control effort weights so as to ensure stability and constraints fulfillment when they are used for LQ control and the state of the plant belongs to a suitable bounded region of the state space. A logic is then used to select on-line the most appropriate control weight according to a state set-membership criterion.
Angeli D, Casavola A, Giannelli M, et al., 1998, Globally stable control of linear plants under positional and incremental actuator saturations, Proceedings of the IEEE Conference on Decision and Control, Vol: 1, Pages: 383-388, ISSN: 0191-2216
A receding-horizon strategy is presented for set-point tracking and global stabilization of asymptotically null controllable plants in the presence of actuators with position and rate limiting constraints. The algorithm, providing an integral action, is able to manage piecewise constant disturbances acting on the system output and state.
Angeli D, Sontag ED, Wang Y, 1998, Remark on integral input to state stability, Proceedings of the IEEE Conference on Decision and Control, Vol: 3, Pages: 2491-2496, ISSN: 0191-2216
Integral input to state stability (IISS) is a notion which generalizes the concept of finite gain with respect to integral norms, in the same manner that input to state stability (ISS) generalizes the idea of finite gain with respect to supremum norms. This paper provides a necessary and sufficient characterization of the IISS property, stated in dissipation terms. It also provides a LaSalle-type invariance principle for ISS.
Angeli D, Casavola A, Mosca E, 1998, Enforcing constraints in industrial control systems: Command governor tools, Pages: 746-750
The problem of constrained control of linear plants is addressed. Some algorithms are proposed that ensure constraints fulfillment and set-point tracking through a non-linear filtering action performed on the reference signal. An application to a D.C. motor is presented to clarify the proposed solutions and illustrate their effectiveness in practice.
Grundelius M, Angeli D, 1996, Adaptive control of systems with backlash acting on the input, Pages: 4689-4694, ISSN: 0191-2216
Two different adaptive controllers for systems with backlash acting on the input are discussed; one in continuous time and one in discrete time. Both schemes are based on a backlash inverse and a linear controller. The unknown plant parameters and the backlash width are estimated. The estimated parameters are used for pole placement design of the controller and for backlash compensation in the backlash inverse. Some analysis of the estimator convergence is done. Simulations of a second order plant show that both schemes give a nice behavior.
This data is extracted from the Web of Science and reproduced under a licence from Thomson Reuters. You may not copy or re-distribute this data in whole or in part without the written consent of the Science business of Thomson Reuters.