1,004 research outputs found
Lagrange Stabilization of Pendulum-like Systems: A Pseudo H-infinity Control Approach
This paper studies the Lagrange stabilization of a class of nonlinear systems
whose linear part has a singular system matrix and which have multiple periodic
(in state) nonlinearities. Both state and output feedback Lagrange
stabilization problems are considered. The paper develops a pseudo H-infinity
control theory to solve these stabilization problems. In a similar fashion to
the Strict Bounded Real Lemma in classic H-infinity control theory, a Pseudo
Strict Bounded Real Lemma is established for systems with a single unstable
pole. Sufficient conditions for the synthesis of state feedback and output
feedback controllers are given to ensure that the closed-loop system is pseudo
strict bounded real. The pseudo H-infinity control approach is applied to solve
state feedback and output feedback Lagrange stabilization problems for
nonlinear systems with multiple nonlinearities. An example is given to
illustrate the proposed method
Leonovâs nonlocal reduction technique for nonlinear integro-differential equations
Starting from pioneering works by Lurâe, Popov and Zames, global stability theory for nonlinear control systems has been primarily focused on systems with only one equilibrium. Global stability criteria for other kinds of attractors (such as e.g. infinite sets of equilibria) are not well studied and typically require special tools, primarily based on the Lyapunov method. Analysis of stability becomes especially complicated for infinite-dimensional dynamical systems with multiple equilibria, e.g. systems described by delay or more general convolutionary equations. In this paper, we propose novel stability criteria for infinite-dimensional systems with periodic nonlinearities, which have infinite sets of equilibria and describe dynamics of phase-locked loops and other synchronization circuits. Our method combines Leonovâs nonlocal reduction technique with the idea of Popovâs âintegral indicesâ and allows to obtain new frequency-domain conditions, ensuring the convergence of every solution to one of the equilibria points
Model-Based Control Using Koopman Operators
This paper explores the application of Koopman operator theory to the control
of robotic systems. The operator is introduced as a method to generate
data-driven models that have utility for model-based control methods. We then
motivate the use of the Koopman operator towards augmenting model-based
control. Specifically, we illustrate how the operator can be used to obtain a
linearizable data-driven model for an unknown dynamical process that is useful
for model-based control synthesis. Simulated results show that with increasing
complexity in the choice of the basis functions, a closed-loop controller is
able to invert and stabilize a cart- and VTOL-pendulum systems. Furthermore,
the specification of the basis function are shown to be of importance when
generating a Koopman operator for specific robotic systems. Experimental
results with the Sphero SPRK robot explore the utility of the Koopman operator
in a reduced state representation setting where increased complexity in the
basis function improve open- and closed-loop controller performance in various
terrains, including sand.Comment: 8 page
Performance-Robust Dynamic Feedback Control of Lipschitz Nonlinear Systems
This dissertation addresses the dynamic control of nonlinear systems with finite energy noise in the state and measurement equations. Regional eigenvalue assignment (REA) is used to ensure that the state estimate error is driven to zero significantly faster than the state itself. Moreover, the controller is designed for the resulting closed loop system to achieve any one of a set of general performance criteria (GPC). The nonlinear model is assumed to have a Lipschitz nonlinearity both in the state and measurement equations. By using the norm bound of the nonlinearity, the controller is designed to be robust against all nonlinearities satisfying the norm-bound. A Luenberger-type nonlinear observer is used to estimate the system state, which is not directly measurable. The choice of the eigenvalue locations for the linear part of the system is based on the transient response specifications and the separation of the controller dynamics from the observer dynamics. Furthermore, the GPC are incorporated to achieve performance requirements such as H2, Hâ, etc. The advantage of using GPC is it allows the designer flexibility in choosing a performance objective to tune the system. The design problem introduced in this dissertation uses various mathematical techniques to derive LMI conditions for the controller and observer design using REA, GPC, and the bounds on the Lipschitz nonlinearities. All work will be demonstrated in both continuous- and discrete-time. Illustrative examples in both time domains are given to demonstrate the proposed design procedure. Multiple numerical approaches are also presented and compared in simulations for ease of use, applicability, and conservatism
Imprecise dynamic walking with time-projection control
We present a new walking foot-placement controller based on 3LP, a 3D model
of bipedal walking that is composed of three pendulums to simulate falling,
swing and torso dynamics. Taking advantage of linear equations and closed-form
solutions of the 3LP model, our proposed controller projects intermediate
states of the biped back to the beginning of the phase for which a discrete LQR
controller is designed. After the projection, a proper control policy is
generated by this LQR controller and used at the intermediate time. This
control paradigm reacts to disturbances immediately and includes rules to
account for swing dynamics and leg-retraction. We apply it to a simulated Atlas
robot in position-control, always commanded to perform in-place walking. The
stance hip joint in our robot keeps the torso upright to let the robot
naturally fall, and the swing hip joint tracks the desired footstep location.
Combined with simple Center of Pressure (CoP) damping rules in the low-level
controller, our foot-placement enables the robot to recover from strong pushes
and produce periodic walking gaits when subject to persistent sources of
disturbance, externally or internally. These gaits are imprecise, i.e.,
emergent from asymmetry sources rather than precisely imposing a desired
velocity to the robot. Also in extreme conditions, restricting linearity
assumptions of the 3LP model are often violated, but the system remains robust
in our simulations. An extensive analysis of closed-loop eigenvalues, viable
regions and sensitivity to push timings further demonstrate the strengths of
our simple controller
On Observer-Based Control of Nonlinear Systems
Filtering and reconstruction of signals play a fundamental role in modern signal processing, telecommunications, and control theory and are used in numerous applications. The feedback principle is an important concept in control theory. Many different control strategies are based on the assumption that all internal states of the control object are available for feedback. In most cases, however, only a few of the states or some functions of the states can be measured. This circumstance raises the need for techniques, which makes it possible not only to estimate states, but also to derive control laws that guarantee stability when using the estimated states instead of the true ones. For linear systems, the separation principle assures stability for the use of converging state estimates in a stabilizing state feedback control law. In general, however, the combination of separately designed state observers and state feedback controllers does not preserve performance, robustness, or even stability of each of the separate designs. In this thesis, the problems of observer design and observer-based control for nonlinear systems are addressed. The deterministic continuous-time systems have been in focus. Stability analysis related to the Positive Real Lemma with relevance for output feedback control is presented. Separation results for a class of nonholonomic nonlinear systems, where the combination of independently designed observers and state-feedback controllers assures stability in the output tracking problem are shown. In addition, a generalization to the observer-backstepping method where the controller is designed with respect to estimated states, taking into account the effects of the estimation errors, is presented. Velocity observers with application to ship dynamics and mechanical manipulators are also presented
Networked Control System Design and Parameter Estimation
Networked control systems (NCSs) are a kind of distributed control systems in which the data between control components are exchanged via communication networks. Because of the attractive advantages of NCSs such as reduced system wiring, low weight, and ease of system diagnosis and maintenance, the research on NCSs has received much attention in recent years. The first part (Chapter 2 - Chapter 4) of the thesis is devoted to designing new controllers for NCSs by incorporating the network-induced delays. The thesis also conducts research on filtering of multirate systems and identification of Hammerstein systems in the second part (Chapter 5 - Chapter 6).
Network-induced delays exist in both sensor-to-controller (S-C) and controller-to-actuator (C-A) links. A novel two-mode-dependent control scheme is proposed, in which the to-be-designed controller depends on both S-C and C-A delays. The resulting closed-loop system is a special jump linear system. Then, the conditions for stochastic stability are obtained in terms of a set of linear matrix inequalities (LMIs) with nonconvex constraints, which can be efficiently solved by a sequential LMI optimization algorithm. Further, the control synthesis problem for the NCSs is considered. The definitions of Hâ and Hâ norms for the special system are first proposed. Also, the plant uncertainties are considered in the design. Finally, the robust mixed Hâ/Hâ control problem is solved under the framework of LMIs.
To compensate for both S-C and C-A delays modeled by Markov chains, the generalized predictive control method is modified to choose certain predicted future control signal as the current control effort on the actuator node, whenever the control signal is delayed. Further, stability criteria in terms of LMIs are provided to check the system stability. The proposed method is also tested on an experimental hydraulic position control system.
Multirate systems exist in many practical applications where different sampling rates co-exist in the same system. The lâ-lâ filtering problem for multirate systems is considered in the thesis. By using the lifting technique, the system is first transformed to a linear time-invariant one, and then the filter design is formulated as an optimization problem which can be solved by using LMI techniques.
Hammerstein model consists of a static nonlinear block followed in series by a linear dynamic system, which can find many applications in different areas. New switching sequences to handle the two-segment nonlinearities are proposed in this thesis. This leads to less parameters to be estimated and thus reduces the computational cost. Further, a stochastic gradient algorithm based on the idea of replacing the unmeasurable terms with their estimates is developed to identify the Hammerstein model with two-segment nonlinearities.
Finally, several open problems are listed as the future research directions
A review of convex approaches for control, observation and safety of linear parameter varying and Takagi-Sugeno systems
This paper provides a review about the concept of convex systems based on Takagi-Sugeno, linear parameter varying (LPV) and quasi-LPV modeling. These paradigms are capable of hiding the nonlinearities by means of an equivalent description which uses a set of linear models interpolated by appropriately defined weighing functions. Convex systems have become very popular since they allow applying extended linear techniques based on linear matrix inequalities (LMIs) to complex nonlinear systems. This survey aims at providing the reader with a significant overview of the existing LMI-based techniques for convex systems in the fields of control, observation and safety. Firstly, a detailed review of stability, feedback, tracking and model predictive control (MPC) convex controllers is considered. Secondly, the problem of state estimation is addressed through the design of proportional, proportional-integral, unknown input and descriptor observers. Finally, safety of convex systems is discussed by describing popular techniques for fault diagnosis and fault tolerant control (FTC).Peer ReviewedPostprint (published version
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