Adaptive and non-adaptive 'pole-placement' control of multivariable linear time-varying plants

Multivariable adaptive control: A survey

“…A detailed study can be found in Limanond and Tsakalis (2001). The direct and indirect multivariable adaptive pole placement control designs presented in this subsection are also applicable to discrete-time systems.…”

“…The direct and indirect multivariable adaptive pole placement control designs presented in this subsection are also applicable to discrete-time systems. More indirect adaptive pole placement control schemes have been developed in Limanond and Tsakalis (2001) for MIMO time-varying plants, including those using internal model principle designs (Ioannou & Sun, 1996) for achieving certain desired tracking performance, in Arruti and Florez (1992) for systems with saturation, in Gibbens et al (1993), Mikles (1990), Nassiri-Toussi and Ren (1997), and Prager and Wellstead (1980) for self-tuning control.…”

“…Adaptive pole placement control can be designed either in a direct adaptive control framework or in an indirect adaptive control framework, for possibly non-minimum phase systems whose zeros may be unstable. Indirect control designs are more commonly seen in the literature (see, for example, Limanond & Tsakalis, 2001), under the solvability condition of a Diophantine equation for control parameters, and some direct control designs have been developed which adaptively update the controller parameters, without the control equation solvability issue but require persistent excitation conditions for closed-loop system stability .…”

“…Such a scheme, simple for the SISO case, needs further study to specify the needed design conditions for the MIMO case. An alternative pole placement control scheme is given in and Limanond and Tsakalis (2001) in a modified form, for A(s) = [I, sI, . .…”

Time-varying high-gain trajectory linearization observer design

“…and output respectively, and the mappings · · · : which can be stabilized using a LTV control law ? oe OÐ>ÑB, with the assumption that the system is strongly controllable [20]. The LTV gain can be computed OÐ>Ñ symbolically using the PD-eigenstructure assignment approach .…”