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In designing feedback controllers for dynamical systems a variety of modern, [[Multivariable calculus|multivariable]] controllers are used. In general, these controllers are often designed at various operating points using [[Linearization|linearized]] models of the [[Scheduling|system dynamics]] and are scheduled as a function of a [[parameter]] or parameters for operation at intermediate conditions. It is an approach for the control of non-linear systems that uses a family of linear controllers, each of which provides satisfactory control for a different operating point of the system. One or more [[observable]] variables, called the [[Scheduling|scheduling variables]], are used to determine the current operating region of the system and to enable the appropriate linear controller. For example, in case of aircraft control, a set of controllers are designed at different gridded locations of corresponding parameters such as [[Angle of attack|AoA]], [[Mach number|Mach]], [[dynamic pressure]], [[Center of mass|CG]] etc. In brief, gain scheduling is a control design approach that constructs a nonlinear controller for a nonlinear plant by patching together a collection of linear controllers. These linear controllers are blended in real-time via switching or [[interpolation]].
Scheduling multivariable controllers can be a very tedious and time-consuming task. A new paradigm is the linear parameter-varying (LPV) techniques which synthesize of automatically scheduled multivariable controller.
===Drawbacks of classical gain scheduling===
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* It is also important that the selected scheduling variables reflect changes in plant dynamics as operating conditions change. It is possible in gain scheduling to incorporate linear [[robust control]] methodologies into nonlinear control design; however the global stability, robustness and performance properties are not addressed explicitly in the design process.
Though the approach is simple and the computational burden of linearization scheduling approaches is often much less than for other nonlinear design approaches, its inherent drawbacks sometimes outweigh its advantages and necessitates a new paradigm for the control of dynamical systems. New methodologies such as Adaptive control based on [[Artificial neural networks|Artificial Neural Networks]] (ANN), [[Fuzzy logic]], [[Reinforcement learning|Reinforcement Learning]],<ref>{{Cite journal |last1=Hosseini |first1=Ehsan |last2=Aghadavoodi |first2=Ehsan |last3=Fernández Ramírez |first3=Luis M. |date=September 2020 |title=Improving response of wind turbines by pitch angle controller based on gain-scheduled recurrent ANFIS type 2 with passive reinforcement learning |url=https://linkinghub.elsevier.com/retrieve/pii/S0960148120307588 |journal=Renewable Energy |language=en |volume=157 |pages=897–910 |doi=10.1016/j.renene.2020.05.060|bibcode=2020REne..157..897H |url-access=subscription }}</ref><ref>{{Cite journal |last1=Yeh |first1=Yi-Liang |last2=Yang |first2=Po-Kai |date=2021-11-26 |title=Design and Comparison of Reinforcement-Learning-Based Time-Varying PID Controllers with Gain-Scheduled Actions |journal=Machines |language=en |volume=9 |issue=12 |pages=319 |doi=10.3390/machines9120319 |doi-access=free |issn=2075-1702}}</ref><ref>{{Cite journal |last1=Gutiérrez-Oribio |first1=Diego |last2=Stathas |first2=Alexandros |last3=Stefanou |first3=Ioannis |date=2024-12-17 |title=AI-Driven Approach for Sustainable Extraction of Earth's Subsurface Renewable Energy While Minimizing Seismic Activity |url=https://onlinelibrary.wiley.com/doi/10.1002/nag.3923 |journal=International Journal for Numerical and Analytical Methods in Geomechanics |language=en |doi=10.1002/nag.3923 |issn=0363-9061|arxiv=2408.03664 }}</ref> etc. try to address such problems, the lack of proof of stability and performance of such approaches over entire operating parameter regime requires design of a parameter dependent controller with guaranteed properties for which, a Linear Parameter Varying controller could be an ideal candidate.
==Linear parameter-varying systems==
LPV systems are a very special class of nonlinear systems which appears to be well suited for control of dynamical systems with parameter variations. In general, LPV techniques provide a systematic design procedure for gain-scheduled multivariable controllers. This methodology allows performance, robustness and [[Bandwidth (signal processing)|bandwidth]] limitations to be incorporated into a unified framework.<ref>{{cite web|last=J. Balas|first=Gary|title=Linear Parameter-Varying Control And Its Application to Aerospace Systems|url=http://www.icas.org/ICAS_ARCHIVE/ICAS2002/PAPERS/541.PDF|publisher=ICAS|accessdate=2013-01-29|date=2002}}</ref><ref>{{cite web|last=Wu|first=Fen|title=Control of Linear Parameter Varying systems|url=
===Parameter dependent systems===
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