· Hankyu Kim · Control · 3 min read
One-shot vs Iteration-based Computation in Control
This post contrasts one-shot (memoryless) control computation with iteration-based, optimization-driven control such as MPC, clarifying their roles, trade-offs, and practical implications in robotics.
Introduction
In control systems, how a controller computes its output is just as important as what it computes. Broadly, control computation can be divided into two paradigms:
- One-shot computation: the control input is computed in a single, direct step.
- Iteration-based computation: the control input is obtained through repeated numerical optimization.
This distinction appears frequently in robotics, autonomous driving, and optimal control, especially when comparing classical controllers such as LQR or PID with optimization-based methods like Model Predictive Control (MPC).
One-shot Computation (Memoryless Control)
One-shot computation refers to control laws that produce an output immediately from the current state or error, without internal iterations or solver loops.
The controller can be expressed as:
where the mapping is fixed and explicitly defined.
Key Characteristics
- No iteration at runtime
- No internal solver or optimization loop
- Often admits a closed-form expression
- Highly predictable computational cost
Typical Examples
- Linear Quadratic Regulator (LQR):
- Proportional or PID control
- Feedforward or inverse-dynamics control
- Explicit MPC solved offline
Strengths and Limitations
- Fast and reliable for real-time systems
- Easy to analyze for stability
- Limited ability to handle constraints
- Less flexible for highly nonlinear or time-varying tasks
One-shot controllers can be interpreted as static state-feedback laws: the controller does not optimize online, it simply evaluates.
Iteration-based Computation (Optimization-driven Control)
Iteration-based computation determines the control input by solving an optimization problem online.
The control action is obtained by repeatedly refining candidate inputs until a locally optimal solution is found:
This process involves multiple numerical iterations per control step.
Key Characteristics
- Numerical optimization loop
- Internal solver state such as warm start
- Trade-off between solution quality and computation time
- Often implemented in a receding-horizon manner
Example: Model Predictive Control (MPC)
Model Predictive Control (MPC) is the canonical example of iteration-based control.
At each control timestep:
- Predict future system evolution using a model.
- Solve a finite-horizon optimization problem:
subject to the system dynamics and constraints:
- Apply only the first control input.
- Repeat the procedure at the next timestep.
Why MPC Is Iteration-based
- The optimization problem is solved numerically
- Each solve requires multiple iterations such as SQP or Gauss-Newton
- Computation time depends on horizon length, constraints, and solver choice
Strengths and Limitations
- Naturally handles constraints
- Suitable for nonlinear and multivariable systems
- Computationally expensive
- Requires careful real-time tuning
What Iteration Means and What It Does Not
Iteration-based computation does not refer to time integration methods such as Euler or RK4.
Instead:
- Iteration refers to repeated improvement of the control input
- The goal is optimality, not numerical accuracy of state propagation
A controller may be one-shot at the control level while still relying on iterative numerical integration internally.
Side-by-side Comparison
| Aspect | One-shot Computation | Iteration-based Computation |
|---|---|---|
| Runtime iterations | None | Multiple |
| Control law | Explicit | Implicit optimization |
| Constraint handling | Weak | Strong |
| Computational cost | Fixed and low | Variable and higher |
| Typical examples | PID | MPC |
Putting It All Together
One-shot computation prioritizes speed, simplicity, and reliability. Iteration-based computation prioritizes flexibility, optimality, and constraint handling.
Modern robotic systems often combine both approaches: iteration-based planners or MPC at lower frequency, and one-shot controllers in the inner high-frequency control loop.
Summary
One-shot and iteration-based computation represent two fundamentally different philosophies in control design.
One-shot controllers compute actions directly from the current state. Iteration-based controllers compute actions by solving an optimization problem online.
Neither approach is universally superior. In practice, effective robotic systems often leverage both paradigms at different layers of the control stack.
