Multiple model adaptive control. Part 1: Finite controller coverings

Robust stability and performance analysis for multiple model adaptive controllers

“…[1], [5], [2]) in multiple model adaptive control are 1. the construction of comprehensive stability, robustness and performance results, and 2. the performance orientated design of candidate plant model sets. Both issues are closely related since the lack of a suitable bounds of global performance precludes fully principled performance orientated design.…”

“…The ideas behind using covers of uncertainty sets as the basis for the design can also be found in e.g. [1], [5]: note that in contrast to these contributions, we establish global performance results based on these covers, hence leading to the promise of a fully principled design methodology [2].…”

Robust stability and performance analysis for multiple model adaptive controllers

“…[1], [5], [2]) in multiple model adaptive control are 1. the construction of comprehensive stability, robustness and performance results, and 2. the performance orientated design of candidate plant model sets. Both issues are closely related since the lack of a suitable bounds of global performance precludes fully principled performance orientated design.…”

“…The ideas behind using covers of uncertainty sets as the basis for the design can also be found in e.g. [1], [5]: note that in contrast to these contributions, we establish global performance results based on these covers, hence leading to the promise of a fully principled design methodology [2].…”

Practical novel tests for ensuring safe adaptive control

“…The simulation results reveal that σ(T ′ (jω)) < 1 ∀ω ≥ 1.8401 rad /s. Given that unwarg det T (j0) = 0 and unwarg det T (jω 0 ) = −0.0079π, the condition in (8) in Theorem 12 holds and hence C 1 is stabilizing. Indeed, computing H(P, C 1 ) confirms that C 1 is stabilizing.…”

The power dissipation method and kinematic reducibility of multiple-model robotic systems

“…Theorem 8.3 [31]: Let : be a compact, set-valued map, and let be a sequence of solutions to the differential inclusion (8) such that . Then, is also a solution to (8).…”

“…Then, is also a solution to (8). Note that solutions to the differential inclusion are, in general, not unique, meaning that there is often an infinite family of solutions.…”

Robust stability and performance analysis for multiple model adaptive controllers

“…[1], [5], [2]) in multiple model adaptive control are 1. the construction of comprehensive stability, robustness and performance results, and 2. the performance orientated design of candidate plant model sets. Both issues are closely related since the lack of a suitable bounds of global performance precludes fully principled performance orientated design.…”

“…The ideas behind using covers of uncertainty sets as the basis for the design can also be found in e.g. [1], [5]: note that in contrast to these contributions, we establish global performance results based on these covers, hence leading to the promise of a fully principled design methodology [2].…”

Practical novel tests for ensuring safe adaptive control

“…The simulation results reveal that σ(T ′ (jω)) < 1 ∀ω ≥ 1.8401 rad /s. Given that unwarg det T (j0) = 0 and unwarg det T (jω 0 ) = −0.0079π, the condition in (8) in Theorem 12 holds and hence C 1 is stabilizing. Indeed, computing H(P, C 1 ) confirms that C 1 is stabilizing.…”

The power dissipation method and kinematic reducibility of multiple-model robotic systems

“…Theorem 8.3 [31]: Let : be a compact, set-valued map, and let be a sequence of solutions to the differential inclusion (8) such that . Then, is also a solution to (8).…”

“…Then, is also a solution to (8). Note that solutions to the differential inclusion are, in general, not unique, meaning that there is often an infinite family of solutions.…”

Robust stability and performance analysis for multiple model adaptive controllers

“…[1], [5], [2]) in multiple model adaptive control are 1. the construction of comprehensive stability, robustness and performance results, and 2. the performance orientated design of candidate plant model sets. Both issues are closely related since the lack of a suitable bounds of global performance precludes fully principled performance orientated design.…”

“…The ideas behind using covers of uncertainty sets as the basis for the design can also be found in e.g. [1], [5]: note that in contrast to these contributions, we establish global performance results based on these covers, hence leading to the promise of a fully principled design methodology [2].…”

Practical novel tests for ensuring safe adaptive control

“…The simulation results reveal that σ(T ′ (jω)) < 1 ∀ω ≥ 1.8401 rad /s. Given that unwarg det T (j0) = 0 and unwarg det T (jω 0 ) = −0.0079π, the condition in (8) in Theorem 12 holds and hence C 1 is stabilizing. Indeed, computing H(P, C 1 ) confirms that C 1 is stabilizing.…”

The power dissipation method and kinematic reducibility of multiple-model robotic systems

“…Theorem 8.3 [31]: Let : be a compact, set-valued map, and let be a sequence of solutions to the differential inclusion (8) such that . Then, is also a solution to (8).…”

“…Then, is also a solution to (8). Note that solutions to the differential inclusion are, in general, not unique, meaning that there is often an infinite family of solutions.…”