19 results on '"Mhaskar, Prashant"'
Search Results
2. Controllability minimum principle based construction of the null controllable region for nonlinear systems.
- Author
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Mahmood, Maaz, Homer, Tyler, and Mhaskar, Prashant
- Subjects
NONLINEAR systems ,MAXIMA & minima ,LYAPUNOV functions ,CONTROLLABILITY in systems engineering - Abstract
The present manuscript addresses the problem of designing a procedure for constructing the null controllable Region (the set of states from where stabilization is achievable subject to constraints). To this end, a controllability minimum principle based computationally tractable approach for constructing the null controllable region is presented. Simulation results are used to illustrate the computation of the NCR for several examples. [ABSTRACT FROM AUTHOR]
- Published
- 2021
- Full Text
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3. A trajectory‐based method for constructing null controllable regions.
- Author
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Homer, Tyler, Mahmood, Maaz, and Mhaskar, Prashant
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PONTRYAGIN'S minimum principle ,LYAPUNOV functions ,LINEAR systems - Abstract
Summary: The problem of determining a system's set of stabilizable states, the null controllable region (NCR), is intricately related to the problem of determining control Lyapunov functions. In this paper, we address the problem of construction of the NCR for control‐affine nonlinear systems with input constraints. To this end, we explain how the boundary of the NCR is covered by time‐optimal trajectories. To construct the NCR, we employ an algorithm based on Pontryagin's minimum principle, which integrates optimal trajectories of a special smooth system in reverse time from the boundary of an initial NCR estimate. We illustrate this algorithm with linear and nonlinear system examples. [ABSTRACT FROM AUTHOR]
- Published
- 2020
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4. Utilizing null controllable regions to stabilize input-constrained nonlinear systems.
- Author
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Homer, Tyler and Mhaskar, Prashant
- Subjects
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CONSTRAINED optimization , *NONLINEAR systems , *LYAPUNOV functions , *ITERATIVE methods (Mathematics) , *COMPUTER algorithms , *LEVEL set methods - Abstract
In this paper, we present a method for control of input-constrained nonlinear systems that offers guaranteed stabilization from the entire null controllable region (NCR). The controller achieves stabilization by using a constrained control Lyapunov function (CCLF) based on this NCR. Prior to online implementation, the level sets the CCLF are constructed using an iterative algorithm. The algorithm works by using an invariance principle to expand an initial quadratic Lyapunov function-based region of attraction. The level sets of this CCLF are then utilized in the control calculations, and in particular, an MPC is formulated that requires the system to go to lower level sets of the CCLF. The proposed MPC thus achieves stabilization from the entire NCR. The proposed approach is first corroborated against existing results for linear systems using two- and three-dimensional linear systems examples. Subsequently, the implementation is shown for two and three dimensional nonlinear systems. [ABSTRACT FROM AUTHOR]
- Published
- 2018
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5. Constrained control Lyapunov function-based control of nonlinear systems.
- Author
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Homer, Tyler and Mhaskar, Prashant
- Subjects
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LYAPUNOV functions , *NONLINEAR systems , *CONTROL theory (Engineering) , *COMPUTER algorithms , *CHEMICAL reactors , *PREDICTIVE control systems - Abstract
In this paper, we present an algorithm to address the problem of guaranteed stabilization of nonlinear systems from the largest set of initial conditions from where stabilization is possible, the so-called null controllable region (NCR), while also handling state constraints and partial unboundedness of the NCR. The controller uses the geometry of the NCR to inform a constrained control Lyapunov function which in turn provides feasibility and stability guarantees. The NCR is produced from a novel iterative growth algorithm that exploits a certain invariance property. The new controller implementation is illustrated using a chemical reactor system and compared to a conventional nonlinear model predictive control (MPC) implementation. [ABSTRACT FROM AUTHOR]
- Published
- 2017
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6. Output-Feedback Lyapunov-Based Predictive Control of Stochastic Nonlinear Systems.
- Author
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Homer, Tyler and Mhaskar, Prashant
- Subjects
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STOCHASTIC analysis , *FEEDBACK control systems , *LYAPUNOV functions , *NONLINEAR systems , *CONSTRAINED optimization - Abstract
This paper considers the problem of output-feedback control of stochastic nonlinear systems. A predictive controller is designed for which stability and feasibility (in a probabilistic sense) are guaranteed from an explicitly characterized region of attraction. The controller's performance is characterized by its risk of allowing destabilizing system behavior. Since the controller design relies on certain convergence properties of the state observer, a compatible stochastic high-gain type observer design is also presented. Finally, simulation results illustrating the efficacy of the design are presented. [ABSTRACT FROM PUBLISHER]
- Published
- 2018
- Full Text
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7. Lyapunov-based offset-free model predictive control of nonlinear process systems.
- Author
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Das, Buddhadeva and Mhaskar, Prashant
- Subjects
LYAPUNOV functions ,NONLINEAR systems ,SIMULATION methods & models ,CLOSED loop systems ,UNCERTAINTY - Abstract
This work considers the problem of control of nonlinear systems subject to uncertainty. To this end, a Lyapunov-based robust model predictive controller (MPC) design is integrated with a moving horizon based offset-free mechanism to enable improved closed-loop performance. Simulation results are presented to illustrate the key ideas of the proposed design. [ABSTRACT FROM AUTHOR]
- Published
- 2015
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8. Constrained control Lyapunov function based model predictive control design.
- Author
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Mahmood, Maaz and Mhaskar, Prashant
- Subjects
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LYAPUNOV functions , *PREDICTIVE control systems , *STABILITY of linear systems , *MATHEMATICAL models of chemical processes , *ACTUATORS - Abstract
SUMMARY This work considers linear systems with input constraints with the objective of designing a controller that guarantees stability from all initial conditions in the null-controllable region (the set of initial conditions from where the system can be stabilized). To this end, a recently developed procedure for construction of constrained control Lyapunov functions is utilized within a Lyapunov-based model predictive controller coupled with an auxiliary control design to achieve stabilization from all initial conditions in the null-controllable region. Illustrative simulation results as well as an application to a nonlinear chemical process example is presented to demonstrate the efficacy of the results.Copyright © 2012 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]
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- 2014
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9. Lyapunov-based model predictive control of stochastic nonlinear systems
- Author
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Mahmood, Maaz and Mhaskar, Prashant
- Subjects
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LYAPUNOV functions , *MATHEMATICAL models , *PREDICTIVE control systems , *STOCHASTIC systems , *NONLINEAR systems , *CHEMICAL processes , *FEEDBACK control systems - Abstract
Abstract: In this work, we design a Lyapunov-based model predictive controller (LMPC) for nonlinear systems subject to stochastic uncertainty. The LMPC design provides an explicitly characterized region from where stability can be probabilistically obtained. The key idea is to use stochastic Lyapunov-based feedback controllers, with well characterized stabilization in probability, to design constraints in the LMPC that allow the inheritance of the stability properties by the LMPC. The application of the proposed LMPC method is illustrated using a nonlinear chemical process system example. [Copyright &y& Elsevier]
- Published
- 2012
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10. A safe-parking and safe-switching framework for fault-tolerant control of switched nonlinear systems.
- Author
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Du, Miao and Mhaskar, Prashant
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NONLINEAR systems , *ACTUATORS , *POLYMERIZATION , *METHYL methacrylate , *CHEMICAL process control , *CHEMICAL reactions , *ALGORITHMS , *LYAPUNOV functions - Abstract
This work considers the problem of handling actuator faults in switched nonlinear systems that transit between multiple modes subject to input constraints. The faults considered preclude the possibility of operation at the nominal equilibrium point in the active mode. For the case where the switching schedule is fixed, a safe-parking scheme is designed, which accounts for the switched nature, to operate the system at temporary equilibrium points during fault-repair time and allow resumption of nominal operation after fault repair. For the case where the switching schedule is adjustable, a safe-switching scheme is designed, which exploits the switched nature, to switch the system to a mode (if exists and available) where nominal operation can be preserved (through control structure reconfiguration when necessary) to continue nominal operation. The proposed framework is demonstrated via a switched process example, as well as application to a polymerisation process of methyl methacrylate. [ABSTRACT FROM AUTHOR]
- Published
- 2011
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11. A safe-parking framework for plant-wide fault-tolerant control
- Author
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Gandhi, Rahul and Mhaskar, Prashant
- Subjects
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FAULT tolerance (Engineering) , *CHEMICAL plants , *ACTUATORS , *NONLINEAR systems , *LYAPUNOV functions , *PREDICTIVE control systems - Abstract
Abstract: This work addresses the problem of handling actuator faults in a chemical plant. We consider a multi-unit nonlinear process system subject to input constraints and actuator faults in one unit that preclude the possibility of operating the unit at its nominal equilibrium point. The interconnected nature of the units in a plant brings forth unique opportunities as well as challenges that simply do not exist when handling faults in isolated units. In particular, the fact that the outlet streams from a faulty unit go through subsequent (well functioning) units raises the possibility of better restricting the effects of the fault to the faulty unit. At the same time, handling a fault in a unit may necessitate appropriate action in the downstream unit, which is not a result of a fault in the downstream unit. To address such issues that arise when handling faults in chemical plants, in this work we present a safe-parking framework (we define, in a previous work on handling faults in isolated units, a safe-park point as an operating point where in the event of a fault, a unit can be operated in a way that prevents onset of hazardous situation and allows smooth resumption of nominal operation) for plant-wide fault-tolerant control. We first consider the case where there exists a safe-park point for the faulty unit such that the effect of safe-parking can be completely rejected (via changing the nominal values of the manipulated variables) in the downstream unit. Steady-state as well as dynamic considerations (including the presence of input constraints) is used in determining the necessary conditions for safe-parking the multi-unit system. We next consider the problem where no viable safe-park point for the faulty unit exists such that its effect can be completely rejected in the subsequent unit. A methodology is presented to simultaneously safe-park the consecutive units. Finally, we incorporate performance considerations in the safe-parking framework and illustrate the implementation of the safe-parking framework using a multi-unit chemical reactor system. [Copyright &y& Elsevier]
- Published
- 2009
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12. TRANSITION FROM BATCH TO CONTINUOUS OPERATION IN BIO-REACTORS: A MODEL PREDICTIVE CONTROL APPROACH AND APPLICATION.
- Author
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Mhaskar, Prashant and Aumi, Siam
- Subjects
ALCOHOL ,MATHEMATICAL optimization ,PREDICTIVE control systems ,LYAPUNOV functions ,DIFFERENTIAL equations ,BIOREACTORS - Abstract
Copyright of Canadian Journal of Chemical Engineering is the property of Wiley-Blackwell and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
- Published
- 2007
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13. Stabilization of nonlinear systems with state and control constraints using Lyapunov-based predictive control
- Author
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Mhaskar, Prashant, El-Farra, Nael H., and Christofides, Panagiotis D.
- Subjects
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NONLINEAR systems , *LYAPUNOV functions , *MOTION control devices , *ELECTRONIC instruments - Abstract
Abstract: This work considers the problem of stabilization of nonlinear systems subject to state and control constraints, for cases where the state constraints need to be enforced at all times (hard constraints) and where they can be relaxed for some time (soft constraints). We propose a Lyapunov-based predictive control design that guarantees stabilization and state and input constraint satisfaction for all times from an explicitly characterized set of initial conditions. An auxiliary Lyapunov-based analytical bounded control design is used to characterize the stability region of the predictive controller and also provide a feasible initial guess to the optimization problem in the predictive controller formulation. For the case when the state constraints are soft, we propose a switched predictive control strategy that reduces the time during which state constraints are violated, driving the states into the state and input constraints feasibility region of the Lyapunov-based predictive controller. We demonstrate the application of the Lyapunov-based predictive controller designs through a chemical process example. [Copyright &y& Elsevier]
- Published
- 2006
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14. Output feedback control of switched nonlinear systems using multiple Lyapunov functions
- Author
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El-Farra, Nael H., Mhaskar, Prashant, and Christofides, Panagiotis D.
- Subjects
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LYAPUNOV functions , *NONLINEAR systems , *SYSTEMS theory , *CHEMICAL processes - Abstract
Abstract: This work presents a hybrid nonlinear control methodology for a broad class of switched nonlinear systems with input constraints. The key feature of the proposed methodology is the integrated synthesis, via multiple Lyapunov functions, of “lower-level” bounded nonlinear feedback controllers together with “upper-level” switching laws that orchestrate the transitions between the constituent modes and their respective controllers. Both the state and output feedback control problems are addressed. Under the assumption of availability of full state measurements, a family of bounded nonlinear state feedback controllers are initially designed to enforce asymptotic stability for the individual closed-loop modes and provide an explicit characterization of the corresponding stability region for each mode. A set of switching laws are then designed to track the evolution of the state and orchestrate switching between the stability regions of the constituent modes in a way that guarantees asymptotic stability of the overall switched closed-loop system. When complete state measurements are unavailable, a family of output feedback controllers are synthesized, using a combination of bounded state feedback controllers, high-gain observers and appropriate saturation filters to enforce asymptotic stability for the individual closed-loop modes and provide an explicit characterization of the corresponding output feedback stability regions in terms of the input constraints and the observer gain. A different set of switching rules, based on the evolution of the state estimates generated by the observers, is designed to orchestrate stabilizing transitions between the output feedback stability regions of the constituent modes. The differences between the state and output feedback switching strategies, and their implications for the switching logic, are discussed and a chemical process example is used to demonstrate the proposed approach. [Copyright &y& Elsevier]
- Published
- 2005
- Full Text
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15. Definition and Utilization of the Null Controllable Region for Model Predictive Control of Multi-Input Linear Systems.
- Author
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Battista, Angela, Mhaskar, Prashant, Li, Mingheng, and Sun, Hui
- Subjects
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LINEAR control systems , *LINEAR dynamical systems , *PREDICTION models , *PREDICTIVE control systems , *LYAPUNOV functions , *SET functions - Abstract
The problem of guaranteeing stability from the entire null controllable region (NCR) for multi-input linear dynamical systems is addressed in the present manuscript. The proposed controller design is inspired by results for single input systems and generalized to multiple input systems. The approach relies on utilizing the level sets of the NCR as level sets of a Lyapunov function. A contractive constraint is incorporated into a model predictive control design, guaranteeing feasibility for any horizon length, and resulting in the NCR as the closed-loop stability region. The proposed method is illustrated using a simulation example. [ABSTRACT FROM AUTHOR]
- Published
- 2021
- Full Text
- View/download PDF
16. On Constructing Constrained Control Lyapunov Functions for Linear Systems.
- Author
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Mahmood, Maaz and Mhaskar, Prashant
- Subjects
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LYAPUNOV functions , *LINEAR systems , *TRAJECTORY optimization , *SYSTEMS theory , *LEVEL set methods , *SYMMETRIC matrices , *MATRICES (Mathematics) , *NUMERICAL analysis - Abstract
This works considers the problem of control of linear systems with input constraints. The notion of control Lyapunov functions (CLFs) is first generalized and relaxed to define a constrained control Lyapunov function (CCLF) and a constructive procedure for CCLF is subsequently presented. [ABSTRACT FROM AUTHOR]
- Published
- 2011
- Full Text
- View/download PDF
17. Predictive Control of Switched Nonlinear Systems With Scheduled Mode Transitions.
- Author
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Mhaskar, Prashant, El-farra, Nael H., and Christofides, Panagiotis D.
- Subjects
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PREDICTIVE control systems , *AUTOMATIC control systems , *NONLINEAR systems , *DIFFERENTIAL equations , *SYSTEMS theory , *LYAPUNOV functions - Abstract
In this work, a predictive control framework is proposed for the constrained stabilization of switched nonlinear systems that transit between their constituent modes at prescribed switching times. The main idea is to design a Lyapunov-based predictive controller for each constituent mode in which the switched system operates and incorporate constraints in the predictive controller design which upon satisfaction ensure that the prescribed transitions between the modes occur in a way that guarantees stability of the switched closed-loop system. This is achieved as follows: For each constituent mode, a Lyapunov-based model predictive controller (MPC) is designed, and an analytic bounded controller, using the same Lyapunov function, is used to explicitly characterize a set of initial conditions for which the MPC, irrespective of the controller parameters, is guaranteed to be feasible, and hence stabilizing. Then, constraints are incorporated in the MPC design which, upon satisfaction, ensure that: 1) the state of the closed-loop system, at the time of the transition, resides in the stability region of the mode that the system is switched into, and 2) the Lyapunov function for each mode is nonincreasing wherever the mode is reactivated, thereby guaranteeing stability. The proposed control method is demonstrated through application to a chemical process example. [ABSTRACT FROM AUTHOR]
- Published
- 2005
- Full Text
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18. Data Driven Economic Model Predictive Control.
- Author
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Kheradmandi, Masoud and Mhaskar, Prashant
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ECONOMIC models , *PREDICTIVE control systems , *LYAPUNOV functions , *LINEAR systems , *NONLINEAR systems - Abstract
This manuscript addresses the problem of data driven model based economic model predictive control (MPC) design. To this end, first, a data-driven Lyapunov-based MPC is designed, and shown to be capable of stabilizing a system at an unstable equilibrium point. The data driven Lyapunov-based MPC utilizes a linear time invariant (LTI) model cognizant of the fact that the training data, owing to the unstable nature of the equilibrium point, has to be obtained from closed-loop operation or experiments. Simulation results are first presented demonstrating closed-loop stability under the proposed data-driven Lyapunov-based MPC. The underlying data-driven model is then utilized as the basis to design an economic MPC. The economic improvements yielded by the proposed method are illustrated through simulations on a nonlinear chemical process system example. [ABSTRACT FROM AUTHOR]
- Published
- 2018
- Full Text
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19. Safe-Parking of a Styrene Polymerization Process.
- Author
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Gandhi, Rahul, Baldwin, Dave, and Mhaskar, Prashant
- Subjects
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STYRENE , *ADDITION polymerization , *LYAPUNOV functions , *PREDICTION models , *PROCESS control systems , *CHEMICAL reactors , *ACTUATORS , *TECHNICAL specifications - Abstract
This work considers the problem of control and fault-handling in living nitroxide-mediated radical polymerization (NMRP) of styrene subject to input constraints. First, a Lyapunov based model predictive controller is designed that allows for an explicit computation of the stability region. Next, a fault in one of the monomer feed streams is considered due to which operation of the reactor at the nominal operating point is no longer possible. It is shown that trying to continue nominal operation using the remaining functioning actuator drives the process to a point resulting in significantly off-spec product. A safe-parking framework is utilized to choose an operating point during fault rectification so that the styrene produced during fault rectification complies with the desired product specifications, and smooth resumption of nominal operation upon fault rectification is achieved. [ABSTRACT FROM AUTHOR]
- Published
- 2009
- Full Text
- View/download PDF
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