When the parameters of a system are slowly time-varying or uncertain, we need a control law that adapts itself under such conditions to give reliable performance. It is different from robust control in the sense that it does not need a prior information about the bounds on these uncertain or time-varying parameters. In general one should distinguish between:

1. Feedforward Adaptive Control
2. Feedback Adaptive Control

There are several broad categories of feedback adaptive control (classification can vary):

• Dual Adaptive Controllers
  • Optimal Controllers
  • Suboptimal Dual Controllers
• Nondual Adaptive Controllers
  • Model Reference Adaptive Controllers (MRACs)
    • Gradient Optimization MRACs
    • Stability Optimized MRACs
  • Model Identification Adaptive Controllers (MIACs)
    • Cautious Adaptive Controllers
    • Certainty Equivalent Adaptive Controllers
      • Nonparametric Adaptive Controllers
      • Parametric Adaptive Controllers
        • Explicit Parameter Adaptive Controllers
        • Implicit Parameter Adaptive Controllers

Another classification can be introduced as well:

1. Adaptive Control Based on Discrete-Time Process Identification
2. Adaptive Control Based on the Model Reference Technique
3. Adaptive Control based on Continuous-Time Process Models
4. Adaptive Control of Multivariable Processes
5. Adaptive Control of Nonlinear Processes

While designing adaptive control system, special consideration is necessary in convergence and robustness issues.

Typical applications of the adaptive control are (in general):

• Self-tuning of subsequently fixed linear controllers during the implementation phase for one operating point;
• Self-tuning of subsequently fixed robust controllers during the implementation phase for whole range of operating points;
• Self-tuning of fixed controllers on request if the process behaviour changes due to ageing, drift, wear etc;
• Adaptive control of linear controllers for nonlinear or time-varying processes;
• Adaptive control or self-tuning control of nonlinear controllers for nonlinear processes;
• Adaptive control or self-tuning control of multivariable controllers for multivariable processes (MIMO systems);

Usually these methods adapt the controllers to both the process statics and dynamics. In special cases the adaptation can be limited to the static behavior alone, leading to adaptive control based on characteristic curves for the steady-states or to extremum value control, optimizing the steady state. Hence, there are several ways to apply adaptive control algorithms.